Mix together the melted butter and the runny honey. Place the cold salmon fillet skin side down and spread the honey/butter over it evenly. Sprinkle with dill weed. Put the wood chips in a smoker box and place on grill. Oil grill grates really well before cooking fish.
Place salmon on grill, skin side up over a medium heat. When the salmon skin begins to curl around the edges and the bottom has good grill marks carefully turn. When the meat through the thickest part flakes easily and reaches an internal temperature of 145 degrees F., remove and serve.
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