Heat a large stock pot over medium heat. Add oil, carrots, onion and red pepper. Cook about 5 minutes. Add chicken and garlic; mix well. Cook until chicken is no longer pink and juices run clear, about 10 minutes.
Stir in chicken broth, coconut milk, curry paste, salt and pepper. Bring to a boil, and simmer 5 minutes. Add noodles, and allow soup to come to a boil again. Reduce heat to low, and simmer about 3 minutes.
Cover, remove from heat, and let stand just until noodles are tender, 5-10 minutes.
Garnish with chopped cilantro, if desired.