Heat the vegetable oil in a large pot over medium-high heat. Add the onion and cook, stirring occasionally, until softened and lightly browned, about 8 minutes. Add the garlic and curry paste and cook, stirring, 1 to 2 minutes. Add the chicken broth, coconut milk and fish sauce; cover and bring to a boil.
Add the bell peppers and noodles and simmer, uncovered, until the noodles are al dente, about 3 minutes. Add the chicken and simmer until just cooked through, about 3 more minutes. Stir in the lime juice and cilantro. Add more fish sauce and lime juice, if desired.