At least 1 hour before smoking, soak wood chips in enough water to cover. Drain before using.
For vinaigrette, in a food processor bowl or blender container combine shallots, rice vinegar, lime juice, sugar, and 1/2 teaspoon salt. With machine running, slowly add oil. Add chives; process or blend with one or two on-off pulses just to mix. Set aside.
Thaw fish, if frozen. Rinse fish; pat dry with paper towels. Sprinkle fish with dill, 1/2 teaspoon salt, and the pepper. Cut several slits in a piece of heavy foil large enough to hold fish. Grease foil; place fish on foil, tucking under any thin edges.
Preheat gas grill. Adjust for indirect cooking over medium heat . Add soaked wood chips according to manufacturers directions. Or wrap in foil and add to grill. Cover and heat about 10 minutes or until chips begin to smoke. Place foil with fish on grill rack over unlit burner. Cover and smoke until fish just flakes easily when tested with a fork. (Allow 15 to 18 minutes per 1/2-inch thickness of fish.)
Stir vinaigrette. In a large bowl pour half of the vinaigrette over mesclun; toss to coat. Divide mesclun among 4 dinner plates. Cut fish into 4 serving-size pieces and arrange on top of mesclun. If desired, pass the remaining vinaigrette. To store any leftover vinaigrette, cover and refrigerate for up to 1 week. Makes 4 servings.