Primary Care Enhancement Act of 2017 This bill amends the Internal Revenue Code to: (1) permit an individual to pay primary care service arrangement costs from a health savings account; and (2) allow an eligible taxpayer enrolled in a high-deductible health plan to take a tax deduction for cash paid into a health savings account, even if the taxpayer is simultaneously enrolled in a primary care service arrangement. Under a "primary care service arrangement," an individual is provided coverage restricted to primary care services in exchange for a fixed periodic fee or payment for such services. For the purposes of certain tax-deductible expenses for medical care, the bill expands the definition of "medical care" to include periodic provider fees paid for a defined set of medical services provided on an as-needed basis.