Sprinkle both sides of the chicken thighs with paprika, sea salt and pepper.
Heat the avocado oil in a large skillet over high on the stove top. Wait for a few minutes for the skillet to heat up until it is sizzling hot.
Place the chicken thighs (or chicken pieces) in the skillet, skin-side down and allow them to brown 3 to 5 minutes per side (or 5-10 minutes total). If the skin becomes too dark too quickly, you can reduce the heat to medium-high heat. Depending on the size of your skillet, you may need to do this step in two batches. I can fit all of eight thighs in my 12-inch nonstick skillet.
While the chicken is browning, add the chopped onion, bell peppers, garlic and carrots to the bottom of the slow cooker.
Transfer the browned chicken to your slow cooker with the rest of the ingredients (crushed tomatoes, broth, and wine). Season everything well with sea salt before giving everything a big stir.
Secure the lid on your crock pot and cook on Low heat for 8 to 10 hours, or High heat for 4 to 6 hours.
When the chicken cacciatore is ready, taste the mixture for flavor and add more sea salt to your personal taste.
Serve chicken cacciatore with your choice of rustic bread, pasta noodles, white rice, or brown rice. For a low-carb option, serve over zucchini noodles, spaghetti squash, or cauliflower rice.