As others have said, the issue is more that you would not get enough of your required nutrients, than anything else. Calories are only a measure of the energy in the food, not of its nutritional value.
Your body is much more capable of adapting to changes in energy input than it is to dealing with an excess (which would require excretion and may have toxic effects) or a deficit (usually with detrimental effects) of a vital nutrient or nutrients.
One of the major benefits of a balanced diet is different foods have different nutrients in different proportions, so things tend to balance out in the course of getting the calories we need for the day. If one eats a particular food exclusively, one would not be able to balance out the nutritional effects of that particular food. Assuming your food of choice provided all the essential nutrients in some quantity, in order to ensure you were getting enough of all the nutrients your body needs to function, you would need to eat much more than the 1000 calories you propose, leading to surplus of some essential nutrients, and an excessive intake of calories. The body would then be subject to the toxic effects from an excess of some micronutrients, and would store the majority of the excessive calories as fat.
It might be possible to keep yourself to a low number of total calories and avoid nutrient deficiency by taking supplements, although I don't know enough about that area of human nutrition to know how safe or effective that would be.
