Cook potatoes in large pot of boiling salted water until tender, 25 to 30 minutes. Drain. Cut potatoes in half; place cut side up on rimmed baking sheet. Press each gently with fork to flatten slightly.
Stir butter, chives, and lemon peel in medium saucepan over medium heat until butter melts; season with salt and pepper. Brush some chive butter over potatoes.
Coat grill rack with nonstick spray. Prepare barbecue (medium-high heat).
Grill potatoes, cut side down, until cut side is crisp and brown, 10 to 12 minutes.
Rewarm remaining chive butter. Transfer potatoes, cut side up, to platter. Drizzle with warm chive butter.