Compost Bins in the chicken run
If you have chickens, then arguable the best position for your compost bins is in the chicken run as chickens do a marvellous job in breaking down organic matter. 
Gardening books often talk about the need to turn the contents of a compost bin over two or three times during  the composting process to aid the breakdown of the organic matter.  However most gardeners rarely turn their compost in their bins, which often results in compost of an
Photo of chickens scratching in compost bin.
Chickens scratching in compost bin.  Not only do they help to break down organic matter they remove many of the weed seeds.
 uneven quality.  But if chickens are allowed access to your compost bins they will turn the compost over hundreds of times during the composting process as they scratch for worms and other food. By doing this they make a wonderfully fine compost as even course woody material is literally torn apart by their actions.

Not only do the chickens help break down organic matter they  remove many of the weed seeds in the material.  And as they scratch they also add their chicken manure,  which is an excellent fertilizer.

Ideally the compost bins should be placed in the chicken run which in turn should be set up right next to the main vegetable patch.  That way you get both the benefits of the chickens scratching and a short as possible distance to cart your green waste.

WARNING - If you have your compost bins in the chicken run do not to put any plants into the bins that are potentially poisonous to chickens.  As a precaution I generally  do not add rhubarb leaves,  potato leaves, deadly nightshade or foxglove. But I am sure there are other plants you can add to this list.  Generally I find that well fed adult chickens instinctively avoid plants that are poisonous, but it is not worth the risk of exposing your flock to such dangers.  If you are planning to put your compost bins in your chicken run then it might be worth while familiarising yourself with the poisonous plants in your area.