Place potatoes in large saucepan and cover with cold water; bring to a boil. Cook 8 to 10 min. or until just tender. Drain and transfer potatoes to foil pan. (Or to cook potatoes on grill, place in foil pan along with ½ in. (1 cm) water. Cover pan with foil. Place on grill preheated to medium-high. Close barbecue lid. Bring water to boil. Cook potatoes just until tender, approx. 8 min. Carefully, remove foil cover; cook off or spoon out remaining water.)
Mix par-cooked potatoes, mushrooms, 3 tbsp (45 mL) oil, mustard, red wine vinegar, thyme and half the salt in the foil pan. Cover with foil. Place on grill preheated to medium. Cook, shaking pan occasionally, 20 to 25 min. or until potatoes are fully cooked.
Meanwhile, coat chicken with remaining oil and salt. Grill 8 to 9 min. per side -- basting with BBQ sauce -- until cooked through and internal temperature registers 165°F (74°C).
Sprinkle goat cheese over the warm potato mixture. Divide onto 4 plates. Top with chicken. Serve with green salad and additional BBQ Sauce for dipping, if desired.
Slide hot foil pan onto baking sheet to transfer from grill to table.