Prepare the grill for direct cooking over medium-low heat (about 350°F) and preheat a perforated grill pan for about 10 minutes.
Cut each sweet potato lengthwise in half, and then cut each half into ¾-inch slices. In a bowl whisk the oil, salt, and pepper and add the potato slices. Toss to combine.
Spread the potatoes in a single layer on the grill pan and grill over direct medium-low heat, with the lid closed, until quite tender when pierced with the tip of a knife, 20 to 25 minutes, turning once or twice. Remove from the grill and cool to room temperature.
Meanwhile, in a large bowl whisk the yogurt, mayonnaise, vinegar, and mustard. Cover and refrigerate until needed.
Add the cooled potatoes and chives to the bowl with the yogurt mixture. Gently stir to combine. Cover and refrigerate for at least 2 hours. Serve chilled.