Heat oil in a large skillet over medium heat. Add onion, red and yellow peppers and sauté, stirring frequently, until vegetables begin to soften, about 5 minutes.
Add curry paste to vegetables and cook, stirring to incorporate, for about 1 minute. Add sliced chicken, sauté in mixture for another minute.
Add coconut milk, bring mixture to a boil. Lower heat and simmer until vegetables are tender and chicken is cooked through, about 10 minutes.
Add basil leaves, reserving a few for a garnish. Serve with cooked quinoa and cucumber salad.