Preheat oven to 400°. In a medium bowl, mix chicken with 2 tbsp. oil, the spices, and 1/2 tsp. salt.
Heat remaining 1 tbsp. oil in a large ovenproof frying pan or cast-iron skillet over medium-high heat. Cook chicken skin side down until skin is crisped, about 4 minutes; transfer to a plate.
Add carrots to pan and cook, stirring often, until starting to soften, about 4 minutes. Add raisins, almonds, and remaining 1/2 tsp. salt. Set chicken skin side up on top of carrots.
Roast until carrots are browned and chicken is cooked through, about 20 minutes.
*Rainbow carrots, sold at farmers' markets and some supermarkets, taste just like regular carrots but add a mix of bright colors.