Cook chicken: In a large skillet, heat olive oil over medium-high heat. Add chicken and cook 3-4 until barely cooked through. Add bell pepper and cook 2 minutes more stirring often.
Add and simmer: Add red curry sauce and brown sugar. Stir to combine. Reduce heat to low and simmer for 3-4 until red pepper is crisp-tender and chicken is cooked through.
Finish: Turn off the heat and stir in basil. Allow basil to wilt for a minute and serve over rice.
