Go to High School, Go to College Act of 2017 This bill amends the Higher Education Act of 1965 to direct the Department of Education to carry out (from July 1, 2017, through June 30, 2023) a program awarding Early College Federal Pell Grants to students to support their enrollment in, and completion of, postsecondary courses offered through early college high schools. Students who would be eligible for a Federal Pell Grant if not for their enrollment in secondary school are deemed eligible for an Early College Federal Pell Grant upon their completion of a full-time postsecondary semester or its equivalent. Students may receive Early College Federal Pell Grants in an amount equal to the cost of not more than four full-time postsecondary semesters or the equivalent while enrolled in postsecondary courses offered by an early college high school. Early College Federal Pell Grants shall count toward the 12-semester, or equivalent, limit on a student's receipt of Federal Pell Grants.