At least 1 hour before grilling; soak wood chips in enough water to cover. Drain before using. Thaw fish, if frozen. Rinse fish and pat dry with paper towels.
Place butter in a small microwave-safe bowl. Microwave on 100 percent power (high) for 30 seconds or until melted. Remove from microwave. Stir in thyme, brown sugar, lemon juice, salt, and pepper. Microwave 30 seconds more to meld flavors. Stir to dissolve sugar. Brush generously over fish.
For a charcoal grill, sprinkle wood chips directly over medium coals. Grill fish, meaty side down, directly over coals for 3 minutes. Turn skin side down. Grill for 5 to 7 minutes more or until fish flakes easily when tested with a fork. (For a gas grill, preheat grill. Reduce heat to medium. Add wood chips according to manufacturer's directions. Place fish on greased grill rack over heat. Cover; grill as above.)
Serve fish with Thyme and Pepper Rice and Grilled Squash, if desired. Makes 6 servings.
Thyme and Pepper Rice and Grilled Squash
Brush sweet peppers and summer squash or zucchini with olive or cooking oil and sprinkle lightly with salt and pepper. Add to grill rack with salmon, turning when you turn salmon. Remove from grill and chop peppers; toss with rice and snipped fresh thyme. Slice squash crosswise and serve with salmon and rice mixture.