Trim fat from brisket. Brush brisket with oil. For rub, in a small bowl stir together paprika, salt, black pepper, cayenne pepper, and thyme. Sprinkle rub evenly over both sides of meat; rub in with your fingers.
Drain wood chips. For a charcoal grill, arrange medium-low coals around a drip pan. Test for low heat above pan. Sprinkle some of the drained wood chips over the coals. Place brisket on grill rack over drip pan. Cover and grill for 3 to 3-3/4 hours or until meat is tender. Add more wood chips every 30 minutes. (For a gas grill, preheat grill. Reduce heat to low. Adjust for indirect cooking. Add wood chips according to manufacturers directions. Place meat on a rack in a roasting pan, place on grill rack, and grill as above.)
Meanwhile, prepare Sweet and Hot Barbecue Sauce or warm bottled barbecue sauce in a saucepan over low heat. Let meat stand for 10 minutes. To serve, slice meat thinly across the grain. Serve with barbecue sauce. Makes 15 servings.
Sweet and Hot Barbecue Sauce
In a large saucepan cook onion; jalapeno chile peppers, and garlic, in 1 tablespoon hot cooking oil until onion is tender. Stir in ketchup, brown sugar, white wine vinegar, orange juice, Worcestershire sauce, and dry mustard. Bring to boiling. Reduce heat and simmer, uncovered, for 10 to 15 minutes or to desired consistency. Makes about 3 cups.