Melt the butter in a large pot over medium heat. Add the onion and cook until softened.
Stir in the garlic and cook 30 seconds.
Add the chicken, green chiles, chicken broth, and spices. Bring to a boil, reduce heat, cover, and simmer 15–20 minutes, until chicken is cooked through.
Remove the chicken and shred it (or cube it), then return to the pot.
Stir in the cream cheese and heavy cream. Add zucchini if using.
Simmer uncovered 10–15 minutes, stirring occasionally, until the chili thickens to your liking.
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