Add the potatoes and reduce the heat to a gentle boil and let boil until the potatoes are just starting to turn tender, 10-15 minutes depending on the size of your potatoes.
Drain and rinse with cold water. Slice into halves.
Fire up your grill for medium-high direct grilling.
Melt the butter in a medium saucepan and stir in the chives and lemon juice. Season with salt and pepper to taste.
Transfer the potatoes to the grill, cut-side down and let grill until just starting to turn golden brown and getting just a little char around the edges. Brush lightly with the butter mixture.
Remove potatoes and transfer to a serving bowl or platter. Drizzle with remaining butter mixture and serve.