In a medium bowl, whisk together the coconut milk, lime juice, lime zest, garlic, soy sauce, ginger (if using), salt, and pepper.
Add the chicken to the marinade and refrigerate for at least 30 minutes or up to overnight for enhanced flavor.
Heat olive oil in a large skillet over medium heat.
Remove the chicken from the marinade (reserve the marinade) and cook for 5–7 minutes per side, or until golden brown and fully cooked through. Transfer the chicken to a plate and set aside.
While the chicken is cooking, cook the rice according to the package instructions. Fluff with a fork once done.
In the same skillet used for the chicken, pour in the reserved marinade.
Bring it to a simmer and cook for about 5 minutes, stirring occasionally, until slightly thickened.
Serve the chicken over a bed of rice.
Drizzle with the warm coconut lime sauce and garnish with fresh cilantro and lime wedges.