Season the chicken generously with salt and pepper. In a large dutch oven, combine the coconut milk, vinegar, soy sauce, garlic and bay leaves. Toss the chicken in the sauce to coat. Bring to a boil, then lower the heat, partially cover and simmer, turning the chicken halfway through, until tender; about 50 minutes
About 10 minutes before the chicken is done cooking, preheat the broiler. In a large pot of boiling, salted water, cook the pasta according to package directions.
Transfer the chicken, skin side up, to a foil-lined baking sheet. Broil until browned, about 5 minutes.
Meanwhile, skim off and discard the fat from the sauce in the dutch oven; discard the bay leaves. Bring the sauce to a boil until slightly reduced and thickened, about 5 minutes. Remove from the heat and stir in the spinach to wilt. Serve the chicken with the spinach and pasta.