Heat a large stock pot over medium heat. Add oil, carrots, onion, and bell pepper. Cook for about 3 minutes. Add chicken and mix well. Add garlic. Cook until chicken is no longer pink in the center and juices run clear, 5 to 10 minutes.

Mix in chicken broth, coconut milk, curry paste, salt, and pepper. Bring soup to a boil, about 5 minutes. Add noodles and allow soup to come to a boil again. Reduce heat to low and simmer about 3 minutes.

Cover the pot, remove from heat, and let sit just until noodles are tender, 5 to 10 minutes.