Laying Workers
Cause
When the hive is queenless, and therefore broodless, for several weeks sometimes some workers develop the ability to lay eggs. It's not actually the lack of a queen, but the lack of brood. But the lack of brood is caused by the lack of a queen. These are usually haploid (infertile with a half set of chromosomes) and will all develop into drones.
Symptoms
Also the laying workers lay these in worker cells, in addition to drone cells and usually lays several in each cell. Laying worker eggs are usually on the side of the cell instead of the bottom except in drone cells. A hive with lots of drones is a symptom of laying workers as are the multiple eggs in the cell.
Sometimes a queen, when she starts laying after a time of not laying, will lay a few double eggs but she usually stops after a day or two. The laying workers will lay three or four to a cell in almost every cell. The difficulty is that the bees think they have a queen (the laying workers) and will not accept one. The laying workers are virtually impossible to find. I have found one in a two frame nuc by studying every bee until I saw one lay, but this is impractical in a full sized hive since there would be too many bees and too many laying workers.
Solutions
Simplest, least trips to the beeyard
Shakeout and forget
In my opinion there are only two practical solutions. The simplest solution if you have several hives and especially if the laying worker hive is a long trip, is just shake all the bees in front of the various other hives and divvy all the combs out to the other hives. This is my preferred method for an outyard or a small hive. It doesn't waste your time and money trying to requeen a hive that is going to reject the queen anyway. This is the method of least time spent on interventions and most predictable outcome.
If you really want to have that many hives, you can pull some frames from them several weeks after the shake out and do a split with some brood from all or several of your hives. A frame of open brood and emerging brood and honey and pollen from each and you'll have a nice split.
Most successful but more trips to the beeyard
Give them open brood
The only other really practical method, in my opinion, is to add a frame of open brood every week until they rear a queen. Usually by the second or third frame of open brood they will start queen cells. This is simple enough when the hive is in your backyard. Not so easy in an outyard 60 miles away.
Other less successful methods
I would do one of the above, but if you want to know every possible method that I've tried, here are the things I have done that sometimes work. Note some appear to be, and are, slight variations of the same theme.
1) If you have several weak laying worker hives and at least one strong queenright hive, put all the laying worker hives on the strong queenright hive. The resulting confusion between several hives will usually settle down to one queenright hive.
2) Put a box with some empty comb on the bottom, a double screen on top of that and the old brood nest on top of that. Put the top entrance in the opposite direction. The field bees will leave the top box and return to the bottom one. After a day you have only nurse bees and the laying worker in the top. Remove them and 24 hours later introduce a queen to the bottom box. Then shake out the top box in front of the other hives and give the honey and pollen back to the original hive. Freeze the drone brood and give it to a strong hive to clean up.
3) Put a queen cell in (either a frame from a hive trying to supersede or swarm or one that you made by queen rearing techniques). Sometimes they will let the queen emerge. Usually they will tear it down.
4) Put a virgin queen in. Just smoke it heavily and run her in. Sometimes they will accept her. Usually they will ball her.
5) Put a laying worker hive over a queenright hive on a double screen board. After about a week, do a newspaper combine. Usually they will accept the queen. Sometimes they will kill the queen in the queenright hive and you now have a very large laying worker hive.
6) Start a nuc with some brood from another hive, if you have one, or just do a shaken swarm from your hive, if it's your only one, and introduce the queen to that nuc. When she's laying nicely and there is open brood in the nuc, do a newspaper combine or, to stack the deck even more, put them on a double screen board for a few weeks and then do the newspaper combine.
7) Put a laying worker hive over a queenright hive on a double screen board and after three weeks, shake the laying worker hive out in front of the queen right hive. This almost always works.
8) Make a queenright nuc from a queen and some brood from a queenright hive. Put the nuc over a double screen board over the laying worker hive. After three weeks do a newspaper combine. Usually this works. Sometimes they kill the queen.
9) Put a frame of emerging brood with a queen in a push in cage in the laying worker hive. When they are no longer biting the cage and killing the emerging attendants, release her. This usually works. Sometimes they will kill the queen.
More info on laying workers
Brood pheromones
It's the pheromones from open brood that suppress the laying workers from developing, but some do anyway. It is NOT the queen pheromone as many of the older books suggest.
See page 11 of Wisdom of the hive:
"the queen's pheromones are neither necessary nor sufficient for inhibiting worker's ovaries. Instead, they strongly inhibit the workers from rearing additional queens. It is now clear that the pheromones that provide the proximate stimulus for workers to refrain from laying eggs come mainly from the brood, not from the queen (reviewed in Seeling 1985; see also Willis, Winston, and Slessor 1990)."
There are always multiple laying workers even in a queenright hive
"Anarchistic bees" are ever present but usually in small enough numbers to not cause a problem and are simply policed by the workers UNLESS they need drones. The number is always small as long as ovary development is suppressed.
See page 9 of "The Wisdom of the Hive"
"Although worker honey bees cannot mate, they do possess ovaries and can produce viable eggs; hence they do have the potential to have male offspring (in bees and other Hymenoptera, fertilized eggs produce females while unfertilized eggs produce males). It is now clear, however, that this potential is exceedingly rarely realized as long as a colony contains a queen (in queenless colonies, workers eventually lay large numbers of male eggs; see the review in Page and Erickson 1988). One supporting piece of evidence comes from studies of worker ovary development in queenright colonies, which have consistently revealed extremely low levels of development. All studies to date report far fewer than 1 % of workers have ovaries developed sufficiently to lay eggs (reviewed in Ratnieks 1993; see also Visscher 1995a). For example, Ratnieks dissected 10,634 worker bees from 21 colonies and found that only 7 had moderately developed egg (half the size of a completed egg) and that just one had a fully developed egg in her body."
If you do the math, in a normal booming queenright hive of 100,000 bees that's 70 laying workers. In a laying worker hive it's much higher.
Michael Bush.
http://www.bushfarms.com/beeslayingworkers.htm
Having recent returned to beekeeping after a 40 year gap with my 15yr old son who has developed 14 hives over the last 2 years. We note that two of his hives seem to have adopted laying worker bees when the initial queen cells failed to develop. 
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