Place a large skillet over a medium heat and add the butter. When the butter has melted, add the onion and saute until translucent, 3 to 5 minutes.
Add the chicken, cream of celery soup, 1/2 can of water and the frozen mixed vegetables. Stir well and cook until just heated through, 3 to 5 minutes. Season with salt and pepper. Pour the mixture into a 9-by-13-inch baking dish.
Arrange the tater tots in tightly packed rows to completely cover the top. Do not press the tots into the mixture; just let them sit on top. Bake until the tot topping is browned and the chicken mixture is bubbly, about 30 minutes, then serve.