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1
Make the rub: combine celery salt, paprika, garlic powder, and pepper in a small bowl; stir to mix (using you fingers works well).
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2
Trim any sinews or excess fat off the chicken breasts and discard.
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3
Rinse breasts under cold running water, then drain and blot dry with paper towels.
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4
Place them in a baking dish; sprinkle with rub all over the chicken breasts on both sides, patting it onto the meat with your fingertips; let the breasts cure in the refrigerator, covered, for 30 minutes to 1 hour.
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5
Set up grill for direct grilling using a two-zone fire and preheat one zone to medium and the other to low (two-zone=preheat half or two out of three burners to medium and the rest on low).
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6
For gas grill-place all the wood chips in the smoker box and run the grill on high until you see smoke, then reduce heat to medium.
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7
When ready to cook, brush and oil the grill grate; place the chicken breasts, skin side down, over the medium zone of the grill; grill until golden brown and cooked through, 6-8 minutes per side or until done.
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8
Lightly baste the chicken breasts with the melted butter as they cook, but don't start until each breast has cooked for 3 minutes on each side.
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9
Move the chicken over to the low zone of the grill if the dripping fat causes flare-ups.
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10
Transfer the grilled chicken breasts to a platter and drizzle any remaining melted butter over them.
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11
Serve with barbecue sauce on the side.
