Long-Term Care Veterans Choice Act This bill authorizes the Department of Veterans Affairs (VA) to enter into contracts to pay for specified veterans (i.e., certain veterans who have service-connected disabilities and require nursing home care) to be placed in medical foster homes at their request. A medical foster home is a home designed to provide non-institutional, long-term, supportive care for veterans who are unable to live independently and prefer a family setting. Veterans receiving such care must agree, as a condition of payment for their care, to accept home health services furnished by the VA. Under the bill, no more than a daily average of 900 veterans may have their care in a medical foster home covered by the VA. The VA must create a monitoring system to assess its workload in carrying out the medical foster home payments. Additionally, the Government Accountability Office must submit to Congress reports that assess the implementation of this program and provide recommendations for improvements.