Preheat an outdoor grill.
First, season each fillet with salt and pepper. Then, brush the mayonnaise on the snapper fillets. In a food processor, combine the parsley, basil, and olive oil. Blend until it is thoroughly pureed. Then brush the parsley-basil puree on top of the mayonnaise layer. Finish by brushing a layer of the chili sauce on top of the paste.
Place the brushed fillets on the grill, and grill the snapper for 10 to 15 minutes, or until the fish is completely cooked.