Separate the components of the rotisserie chicken, cutting the meat into bite-sized pieces and skin into strips.

Arrange skin strips on a parchment-lined baking sheet and preheat the oven to 350°F (175°C). Bake for 10-13 minutes until crispy.

Zest and juice the limes to yield about 1/4 cup of lime juice.

In a large 6-quart pot, heat duck fat over medium-high heat.

Add all spices and toast for about 1 minute until fragrant.

Pour in chicken stock and whisk to combine.

Cut cream cheese into chunks and add to the pot, whisking until incorporated and smooth.

Bring the mixture to a gentle boil, then reduce heat and let it simmer for about 5 minutes.

Turn off the heat and stir in the chopped chicken, lime zest, and lime juice.

Ladle chili into bowls and top with crispy skin chips, a dollop of sour cream, cilantro, and lime wedges.