As a child, Chambers saw first hand the effects of discrimination when his father's auto repair business became a target of racial injustice in 1948.

Chambers has said that this experience made him resolved to pursue a career in law, in order to help end segregation and racial discrimination.

[1] After graduating from high school in 1954 (the same month as the landmark Brown v. Board of Education ruling), he enrolled at North Carolina Central University.

With fellow founding partners James E. Ferguson II and Adam Stein, along with lawyers from LDF, the firm successfully litigated a number of key cases before the Supreme Court of the United States that would help to shape evolving American civil rights laws, including: the school busing decision in Swann v. Charlotte-Mecklenburg Board of Education (1971); and two important Title VII employment discrimination cases Griggs v. Duke Power Co. (1971) and Albemarle Paper Co. v. Moody (1975).

On November 22, 1965, in the midst of the first hearings of the Swann school busing case, Chambers's home was bombed along with three other homes of African American leaders: then North Carolina NAACP President Kelly Alexander Sr, his brother Frederick Alexander (a Charlotte city councilman), and community activist Reginald Hawkins.

In 1984, he left the Charlotte firm to again join the NAACP Legal Defense Fund in New York City, this time as its highest executive (Director-Counsel).

Under Chambers' leadership, the LDF litigated cases in the areas of education, voting rights, capital punishment, employment, housing and prisons.

Chambers authored or contributed to a number of important articles and books on civil rights law, including: "Beyond Affirmative Action" (1998), "Race and Equality: The Still Unfinished Business of the Warren Court," The Warren Court: A Retrospective (1996), "Afterward: Racial Equity and Full Citizenship, The Unfinished Agenda," African Americans and the Living Constitution (1996), "Black Americans and the Courts: Has the Clock Been Turned Back Permanently?," The State of Black America (1990), and "Adequate Education for All: A Right, An Achievable Goal" (1987).