Once while we had visitors and my boys were showing them different hens one laid an egg while she was in my son's arms.  I don't know who was the most surprised, me, my son, our visitors, or the hen.
Another strange spot is now being used by a broody hen.  I have a tall wire pen, about 3' square and 5' high, that is occasionally used to house meat birds for their final week.  I placed a sheet of corregated metal on top of that pen to shed the rain, and later placed the roof of a plastic dog house on top of the metal sheeting to keep it from blowing off in the wind.  One day we noticed a bantam hen clucking & bukking up there, and found a few eggs in the space between the plastic dog house roof & the metal sheet!  It has proved to be a popular spot for several hens, so I put some straw in there to cushion & hold the eggs in place.
Now a broody hen has decided to incubate a clutch of eggs in that spot.  No other hens bother her there.  I put some food & water up there for her easy access, so she only needs to come to the ground to poop & dust bathe.  I'm curious to see what will happen after the chicks hatch.  My guess is that they'll hop/fall to the ground, and the hen will then select a new nest spot much closer to the ground for them.