Health Care Quality Improvement Act of 1986 - Provides protection from liability under any Federal law for members of a professional peer review body who, in good faith, take actions which adversely affect the clinical privileges or professional society membership of a physician if such actions are certified by a State review committee. Directs the Secretary of Health and Human Services to designate a State review committee for each State. Requires any entity (including insurance companies) making a payment in a medical malpractice action to report certain information to the Secretary, including: (1) the name of the physician or health care provider; (2) the amount of the payment; and (3) the name of any hospital with which the physician or health care provider is associated. Provides an exception from such reporting requirements where the payment is less than $35,000. Requires each State licensing board which revokes or suspends a physician's license for reasons relating to the physician's professional competence or conduct to report such information to the Secretary. Requires hospitals participating in the Medicare program to obtain certain information from the Secretary regarding staff physicians (or physicians being considered for staff positions). Directs the Secretary to make such information available to State licensing boards. Directs the Secretary to study and report to the Congress on the feasibility and desirability of expanding the information reported under this Act.