Fragile X Research Breakthrough Act of 1999 - Amends the Public Health Service Act to require the Director of the National Institute of Child Health and Human Development to: (1) expand, intensify, and coordinate the Institute's activities respecting research on the disease known as fragile X; (2) make grants to, and enter into contracts with, public or nonprofit private entities for the development and operation of at least three centers to conduct research for improving the diagnosis and treatment of, and finding the cure for, fragile X. Requires each such center assisted to conduct basic and clinical research, which may include clinical trials of new or improved diagnostic methods and drugs or other treatment approaches. Allows such centers to use grant funds provided under this Act to provide fees to individuals serving as subjects in clinical trials.

Requires the Director to provide for the coordination of the centers' activities, including the exchange of information. Requires each center to use the facilities of a single institution, or be formed from a consortium of cooperating institutions.

Allows support to be provided to a center for a period not exceeding five years with authorized extensions.

Authorizes appropriations.

Directs the Secretary of Health and Human Services to establish a program under which the Federal Government enters into contracts with qualified health professionals who agree to conduct research on fragile X in consideration of the Government's agreement to repay, for each year of such service, no more than $35,000 of the principal and interest of the educational loans owed by such health professionals. Authorizes appropriations.