Serving our Rural Veterans Act of 2017 This bill authorizes the Department of Veterans Affairs (VA) to pay for the training and employment of Veterans Health Administration medical residents and interns at a covered facility, which includes: (1) a VA facility; (2) a facility operated by an Indian tribe, a tribal organization, or the Indian Health Service; (3) a federally-qualified health center; or (4) a community health center. (Currently, such payments are authorized only for VA facilities.) The VA shall carry out an eight-year pilot program to establish or affiliate with graduate medical education residency training programs at not more than four facilities. The VA shall reimburse each participating facility for the costs of: curriculum development; recruitment, training, supervision, and retention of residents and faculty; accreditation of education programs; faculty salaries attributable to program activities; and other expenses relating to providing medical education under the program. A program participant: (1) shall agree to one year of obligated service at a covered or a VA facility for each year of partipation in the program, (2) who fails to satisfy the obligated service period shall be liable to the United States for a prorated portion of the amount paid for program participation, and (3) during the period of obligated service, shall be eligible for participation in the Indian Health Service Loan Repayment Program and the VA Education Debt Reduction Program. A covered facility for pilot program purposes means a facility: (1) operated by an Indian tribe, a tribal organization, or the Indian Health Service that has an existing reimbursement agreement with the VA; and (2) located in a rural or remote area.