I had a chicken like this last weekend (curly sue)... I believe it is called Prolapse sp?
It indeed was an egg trying to come out. I heard it could happen to overweight chickens,
too much fat not not enough muscle. (curly sue is handicapped with a near broken neck)
I also heard about the warm bath (soak their butt in warm water) and then slather on some type of lube,
I used antibiotic ointment after the first bath as well as a good drying with the hair dryer (which she loved),
and general purpose lube (from the farm supply) During the 2nd bath the next day.
2nd bath did the trick to loosen the egg, as well as I had the hand held hooked up n the shower
and directly squirted her vent with warm water, she started pushing for me and i eased my fingers
around the back of the lump from outside, and helped her push
...it was an exciting moment when she laid that egg, we both felt better.
However I have also heard that this can happen again, so if you can help the egg out,
then re-acces the situation, Curly sue acted like she needed to lay another the next day too..
If I could have called a local vet for help I would have.
The guy at the feed store also suggested worming them with "wazine" too