Heat coconut oil in a large skillet over medium heat.
Add the chicken and cook until mostly done, about 5-7 minutes.
Add chopped onion, minced garlic, and ginger to the skillet and sauté until onion is translucent, about 5 minutes.
Stir in the red bell pepper and cook for an additional 3 minutes.
Stir in Thai red curry paste and cook for 2 minutes. Add coconut milk, vegetable broth, soy sauce, salt, and brown sugar. Bring to a simmer.
Add chopped carrots and snap peas to the skillet. Simmer for 10-15 minutes or until vegetables are tender.
Stir in chopped basil and lime juice. Season to taste with more curry paste or salt if needed. Serve hot over cooked jasmine rice.