Soak 3 cups of oak, mesquite, or hickory wood chips in water for 1 hour and then drain.
Blend thyme leaves, garlic cloves, dried oregano, and coarse salt in mini processor until garlic is finely chopped. With processor running, gradually add lemon juice, then olive oil. Season herb sauce to taste with pepper and transfer to a bowl. Can be made one day ahead and refrigerated.
Sprinkle roast generously on both sides with salt and pepper. Let stand at least 30 minutes and up to 2 hours.
Prepare barbecue to medium-high heat. If using gas grill, wrap wood chips in foil; pierce foil all over with fork. Remove top grill rack, place foil packet directly on burner, and replace grill rack. Place roast over packet and grill uncovered for 6 minutes (wood in foil will begin to smoke). Turn roast over. Move to spot on grill where heat is indirect and medium-hot. Cover grill and cook until meat thermometer inserted into thickest part of roast registers 128 degrees to 135 degrees for medium-rare, turning roast occasionally, about 13 minutes.
If using charcoal grill sprinkle wood chips over coals and plac roast on rack. Cook roast uncovered 7 minutes. Turn roast over. Move roast to spot on grill where heat is indirect and medium hot. COver grill and cook until thermometer inserted into thickest part of roast registers 128 degrees to 135 degrees for medium-rare, turning roast occasionally, about 13 minutes.
Transfer roast to platter. Let stand 10 minutes. Thinly slice across grain. Serve, passing sauce separately.