Combine olive oil, lime juice, basil, salt, and pepper in a bowl.
Put tilapia fillets in a deep dish and pour the marinade over the top so the fillets are coated well. Refrigerate for 25-30 minutes.
Put grill on medium high. Remove the fillets from the dish pour the marinade into a saucepan. Bring the marinade to a boil, immediately reduce the heat, and let simmer on low for 5 minutes. Remove from heat, cover, and keep warm.
Grill each side for about 5 minutes, or until opaque.