Wash basil and pat dry. Drain pineapple juice from can, reserving the chunks for the skewers. (You will only use about half, so go ahead and put the other half in a reusable container, or eat them.)
Put basil, pineapple juice, olive oil, salt, and three cracks of pepper into a food processor or blender. Process until basil is thoroughly chopped and integrated through liquid. Pour into a large bowl. If you want to reserve some of the marinade in a separate bowl for basting, do it now.
Cut chicken into chunks approximately 1 inch by 1 inch. Put into bowl of marinade. Cover with plastic wrap and put in refrigerator for at least an hour.
When ready to cook, put bamboo skewers into a shallow container of water and let soak. Chop onion and pepper into large pieces on a clean cutting board.
Remove skewers from water and thread chicken, onion, pineapple, pepper, and tomato in an alternating pattern. Place finished skewers on a large plate, and repeat until you’re out of chicken.
Grill over a medium-hot flame for 15 minutes or until a thermometer inserted into a piece registers 165°F.
Be sure to chill any leftovers within two hours of cooking.