In a large skillet, heat the vegetable oil over medium-high heat. Add the chicken pieces, season with salt and pepper, and cook until browned, about 5-7 minutes.
Reduce the heat to medium and add the minced garlic and grated ginger to the skillet. Sauté for 1-2 minutes until fragrant.
Pour in the coconut milk, fish sauce, brown sugar, and lime juice. Stir to combine and bring to a gentle simmer.
Let the mixture simmer for about 10 minutes, stirring occasionally, until the chicken is cooked through and the sauce has thickened slightly.
Stir in the chopped basil and cook for an additional 2 minutes until the basil is wilted.
Serve the coconut basil chicken over cooked rice and enjoy!