William H. Gray, III, College Completion Challenge Grant Program of 1999

William H. Gray, III, College Completion Challenge Grant Program of 1999 - Amends the Higher Education Act of 1965 to establish the William H. Gray, III, College Completion Challenge Grant Program to assist higher education institutions to help at-risk students stay in school and complete their four-year postsecondary academic programs.

Authorizes the Secretary of Education to make competitive matching grants to such institutions or consortia (which may include associate degree-granting institutions belonging to a consortium that also includes baccalaureate degree- granting institutions). Limits to two the number of such grants to any institution.

Requires institutions to use grant funds to provide services or assistance to students, particularly economically disadvantaged students, at risk of leaving their programs of study without baccalaureate degrees. Requires this to be done through one or both of the following: (1) intensive summer programs for incoming first-year students (and, under certain conditions, second- or third-year students); and (2) student support service programs, targeted to students in their first two years of postsecondary education. Allows institutions, if they carry out either or both of those required programs, to use such funds also for grants to students in their first two years of postsecondary education. Allows use of such funds to serve students who have completed their first two years of postsecondary education if they are at-risk and the institution will first meet the needs of all its eligible first- and second-year students for services under this Act.

Authorizes appropriations.