Add andouille to cold pan with a little bit of a neutral oil, place over medium heat and cook until fully cooked and all the fat has rendered out. Remove from pan but leave all the fat behind!
Add diced chicken, season with salt, saute in the andouille fat until chicken has taken on some color and is mostly cooked. Remove and set aside with the cooked andouille.
Next we're going to add out butter in and let this melt all the way. Once butter is fully melted, were going to add our flour and make a roux.
We are going to cook the roux out until it reaches what is called a brown roux. This must be stirred constantly so it does not burn. As the roux cooks, it is going to get darker and thinner. Don't worry this is normal! You'll know when the roux is done because the color will resemble a dark peanut butter and have a rich, nutty aroma. Kind of like burnt popcorn! This will take about 15 minutes.
Add your onion, celery, peppers and garlic. Continue to stir and let these sweat out for about 2 minutes.
Add your spices, let toast for about 30 seconds to a minute.
Gently pour in your chicken stock, stirring to incorporate fully. Allow to come up to a simmer. The roux will begin to thicken the chili now. Lower heat down to low, and add the chicken base, chicken and chorizo back into the pot.
Allow this to cook for about a half an hour so all the flavors develop. Make sure to stir frequently so it doesn't scorch on the bottom!
Add in your half & half and beans now. Return to a simmer.
Add Lime Juice from 1 lime, a couple dashes of tabasco and check your salt. This is ready to serve now.