Heat 1 tablespoon oil in a skillet. Add onion and cook until softened, about 2 minutes. Add bell peppers and zucchini and cook for 5 minutes. Remove vegetables from the skillet.

Heat remaining 1 tablespoon oil in the skillet and add curry paste. Cook and stir for 30 seconds. Add chicken and cook until seared on all sides, about 5 minutes. Return vegetables to the skillet. Stir in peas and green beans. Pour in coconut milk and bring to a boil. Simmer until vegetables are soft and chicken is cooked through, about 15 minutes. Season with salt.