In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until translucent. Stir in the minced garlic and chopped jalapeno pepper, cooking for an additional 1-2 minutes until fragrant.
Add the cubed chicken to the skillet. Sprinkle the curry powder, chili powder, salt, and pepper over the chicken. Stir well to coat the chicken with the spices. Cook for about 5-7 minutes until the chicken is no longer pink.
Pour in the coconut milk and chicken broth, stirring to combine. Bring to a simmer and let it cook for another 10-15 minutes to meld the flavors.
Once the curry has thickened slightly, remove it from the heat and gently fold in the torn basil leaves.
Serve the Coconut Basil Chicken Curry over rice or with naan, garnished with additional basil if desired.