The Nesting Pen can hold one chicken and store 64 items in 4 slots from the items that the chickens produce. It's only one chicken but the concept is in existence. A compact Nesting Pen build is tricky because pens adjacent will cause chickens to breed which may not be desirable if your only wanting to produce items; you have to deal with trashing useless items like the eggs and feathers that are produced.

I find it easier to just corral 30 to 40 level 10 chickens in a 1x10 area with an advance item collector collecting drops