In a 4-quart Dutch oven, combine broth and curry paste. Cover and bring to boiling.
Meanwhile, slice chicken breasts crosswise into 1/4-inch strips; sprinkle lightly with salt and set aside.
Add noodles, sweet potato, and tomato to broth mixture. Return to boiling; reduce heat. Cover and simmer for 2 minutes, stirring once to break up noodles.
Add chicken. Return to boiling; reduce heat. Cover and simmer for 2 to 3 minutes more or until chicken is tender and no longer pink. Stir in coconut milk. Top each serving with cilantro. Makes 6 servings.