Whisk together 1 tablespoon olive oil, honey, salt, and pepper in a large bowl. Add carrots and toss to coat. Place carrots in the air fryer basket in a single layer, in batches, if needed.
Cook in the air fryer at 390 degrees F (200 degrees C), stirring once, until tender, about 10 minutes. Transfer warm cooked carrots to a large bowl, add balsamic glaze and butter, and toss to coat. Sprinkle with chives and serve.