3 tablespoons olive oil, divided
1 shallot, finely chopped
1 tablespoon (or more) red wine vinegar
Kosher salt, freshly ground pepper
2 tablespoons chopped fresh chives
Cut half of cherry tomatoes in half. Heat 1 tablespoon oil in a medium saucepan over medium heat. Add shallot and cook, stirring often, until softened, about 4 minutes. Add halved and whole tomatoes and cook, stirring occasionally, until beginning to release juices, 4–6 minutes. Mash some of tomatoes with a spoon. Add 1 tablespoon vinegar and remaining 2 tablespoons oil; season with salt and pepper. Serve warm or room temperature; add chives just before serving. DO AHEAD: Vinaigrette can be made (without chives) 2 days ahead. Cover and chill. Bring to room temperature and stir in chives.