Preheat the oven to 390°F (200°C). Rub the potatoes lightly with olive oil and place them on a baking sheet.
Bake for about 50 minutes, or until the potatoes are very soft when pierced with a knife. Transfer to a rack and let cool for 10–15 minutes.
Cut off the top quarter of each potato. Carefully scoop out the flesh, leaving about a ¼-inch shell. Place the potato flesh into a mixing bowl.
Add the goat cheese, half and half, chopped chives, salt, and pepper. Gently mash until smooth and creamy.
Fill the potato shells with most of the mashed potato mixture. Pipe or spoon the remaining filling on top for a decorative finish.
Return the potatoes to the baking sheet and broil for about 5 minutes, until heated through and lightly golden on top. Serve warm.