Rinse chanterelles, gently rubbing mushroom gills with fingers to release any grit; drain. Repeat if necessary. Trim and discard bruised parts and discolored ends. Slice mushrooms 1/4 inch thick.
In a 10- to 12-inch pan over high heat, stir mushrooms, 1 tablespoon olive oil, 1 teaspoon vinegar, and thyme until liquid is evaporated and mushrooms are browned, 15 to 20 minutes. Add 2 tablespoons olive oil, the remaining vinegar, and salt and pepper to taste.
Meanwhile, brush bread slices with remaining 1 tablespoon olive oil and lay on a 14- by 17-inch baking sheet. Bake in a 350° oven until crisp and brown, about 15 minutes.
Top toast pieces equally with mushroom mixture and sprinkle with chives.