Long-Term Care Veterans Choice Act This bill authorizes the Department of Veterans Affairs (VA) to enter into contracts to place certain disabled veterans in medical foster homes at the request of such veterans. Specifically, the bill concerns veterans with service-connected disabilities to whom the VA is required to provide nursing home care. Medical foster homes are homes designed to provide non-institutional, long-term, supportive care for veterans who are unable to live independently and prefer a family setting. In any year, not more than a daily average of 900 veterans placed in a medical foster home may have their care covered.