1. Preheat grill to medium-high. On stove, bring a pot of salted water to a boil. In a bowl, toss shrimp, tomatoes, chile and garlic with 1 Tbsp. oil, 1/2 tsp. salt and 1/4 tsp. pepper. Place mixture on a large rectangle of heavy-duty foil. Gather edges to form a rim. Pour in wine, then gather and seal edges to form a packet.
2. Grill packet, shaking occasionally, until shrimp are just pink and opaque, 8 to 10 minutes. Remove packet from grill. Let rest for 5 minutes.
3. Cook pasta for 2 minutes or according to package directions. Top with shrimp mixture and basil and serve.