Whisk together the oil, vinegar, garlic paste and thyme in a medium bowl, add the tomatoes and toss to coat. Let tomatoes sit at room temperature for 30 minutes to marinate.

Heat the grill to high.

Remove the tomatoes from the marinade and skewer 4 per skewer, depending on the size of the tomatoes). Season on both sides with salt and pepper and grill until golden brown and slightly charred on both sides, about 6 minutes. Transfer the skewers to a platter and garnish with chives.