Heat oil in a large skillet over medium heat. Add brussels sprouts and carrots; saute until sprouts start to turn golden brown, about 3 minutes. Add raisins and chicken broth; continue cooking, stirring occasionally, until sprouts are tender when pierced with a paring knife, about 12 minutes. If the skillet becomes too dry before sprouts are tender, add up to 3 tablespoons water, and continue cooking. Remove from heat, and season with salt and pepper. Serve hot.