Chicken coop - chicken is an adjective. To coop. So it's singular. Shoe store. Button basket. Adjectives are always singular. The noun they are modifying gets the plural-ness.
And we say cat harnesses, too, because if something goes plural, its the thing the adjective is describing, not the adjective that goes plural.
Chicken for dinner - chicken is an indefinite noun. Too, most of the words for things-on-the-table are singular because they are indefinite.
Things/nouns that we're likely to say 'some' with, are generally indefinite. 'Some chicken'. I'm buying some chicken. I'm buying chicken - about equivalent.
I might say I'm going to buy some chicken THIGHS or WINGS - again, thighs or wings is the noun, chicken is the adjective.
We don't say I'm going to the store to buy some beefs, or porks. We say hot dogs, or roasts, or t bone steaks, though, because those are units.