Accessible Care by Curbing Excessive lawSuitS Act of 2017 or the ACCESS Act of 2017 This bill establishes provisions governing health care lawsuits where coverage for the care was provided or subsidized by the federal government. The bill does not preempt certain state laws and federal vaccine injury laws and rules. The statute of limitations is three years after the injury or one year after the claimant discovers the injury, whichever occurs first, with exceptions. Noneconomic damages are limited to $250,000. Juries may not be informed of this limitation. Courts must supervise the payment of damages and may restrict attorney contingency fees. The bill sets limits on contingency fees. Certain evidence regarding collateral source benefits (e.g., insurance payments) may be introduced in lawsuits involving injury or wrongful death. The bill provides for periodic payment of future damage awards. A health care provider who prescribes, or dispenses pursuant to a prescription, a medical product approved by the Food and Drug Administration may not be a party to a liability lawsuit or class action lawsuit regarding the product. Expressions of apology, fault, or sympathy by health care providers or their employees to patients or their relatives or representatives regarding suffering, injury, or death from an unanticipated outcome of care are inadmissible as evidence of liability. A person must give a health care provider 90 days' notice before commencing a lawsuit, with exceptions. An affidavit of merit signed by a health care professional who qualifies as an expert witness must be filed simultaneously with a lawsuit. The bill establishes qualifications for expert witnesses.