Thanks for the question!
I had a similar question over on cgSociety, so I’ll repost it here 
We actually started originally working with Iryna Korshak (https://www.behance.net/IraKorshak) quite a while ago. I had seen her art on Behance and thought it looked really beautiful - and absolutely loved her rooster drawings!
As a test, I tried modeling one of the roosters in Blender and we tried texturing it… just to see if we could get the look. Once I felt confident we could match her artwork and design in a model, I reached out to her to see if she would be interested in designing a chicken in the same style. We hired her to do that and then pretty soon she was involved with helping design the look of the entire project!
So the modeling of the car and environments was done not long after that, but then we sat on the project for a while because other items were coming up which were taking presidence. About 2 months before siggraph we started back in on it, remodeling the chicken - then haley started working on the textures.
By mid June I had a rigging plan in place, and was starting to figure out how to use the Bendy Bones in Blender. I was learning the rigging aspect of Blender as I was going, so there was a little trial and error, but for the most part I had the neck planned by the 24th of June. Then I re-worked the neck feathers (initially they were going to be modeled as thick geo - but ended up using planes with textures).
By july 1st, we had a complete rig and texture for the chicken.
The initial animation for the farm shot was done in a day, but after finding the music I went back later and added a few things. So it was probably a total of 2-3 days of animating for the farm shot (including the birds, the sheep motion, etc). Lighting was pretty quick on that because Haley is amazing and the art direction was so specific and perfect.
The chicken’s car rig was also done in a day or so - not too long, since it was a relatively simple rig - the “tough” part was figuring out the squash on the tires - and learning to use the constraints correctly. 
I think by July 10th the short was pretty much done, then it was just animating the title sequence (lots of fun to animate a chicken dancing!) and then just rendering and tweaking. Haley did the comps and was able to whip those out pretty quick… again, because she’s a rock star.
So all in all, most of the production part was done in just a few weeks, with some early production work of modeling the environments, textures, building & rigging the secondary cars, etc done earlier in the year, probably taking just a few weeks of desk time (spread out).
That’s a long answer to your question… but hope it makes sense! 