In a large pot, combine the chicken broth, coconut milk, red curry paste, fish sauce, and lime juice. Bring to a simmer over medium heat.
Add the shredded chicken, bell peppers, carrots, and snap peas to the pot. Cook for about 5-7 minutes, until the vegetables are tender.
Meanwhile, prepare the rice noodles according to package instructions. Drain and set aside.
Once the vegetables are cooked, add the cooked rice noodles to the soup and stir gently to combine.
Serve hot, garnished with sliced green onions, fresh cilantro, and lime wedges on the side.