Heat the vegetable oil in a large skillet or wok over medium heat.
Add the chopped onion and sauté until softened, about 3-4 minutes.
Stir in the minced garlic and grated ginger, and cook for an additional minute until fragrant.
Add the chicken pieces to the skillet, cooking until they are browned on the outside (about 5-7 minutes).
Mix in the red curry paste, stirring well to coat the chicken and onion mixture.
Pour in the coconut milk and chicken broth. Bring to a simmer.
Add the sliced bell peppers and snap peas, along with the fish sauce and brown sugar. Stir to combine.
Let the curry simmer for about 15 minutes, or until the chicken is fully cooked and the vegetables are tender.
Taste and adjust seasoning with salt and pepper as desired.
Serve the coconut curry chicken with rice or naan bread, garnished with fresh cilantro and lime wedges.