However, Moore was a native of Atlanta, spending his youth in the elite black community centered around Auburn Avenue. He had first become interested in law after seeing Thurgood Marshall speak at the NAACP’s national convention in Atlanta in 1951, and after attending law school at Boston University, he returned to his hometown to work on behalf of the African American freedom struggle. Important cases that put him in contact with some of the most important figures of the civil rights movement filled the early years of Moore’s career.

In 1966, for example, the Georgia House of Representatives refused to seat the newly elected Julian Bond because he had voiced support for a Student Non-violent Coordinating Committee (SNCC) statement against the Vietnam War in his capacity as the organization’s communications director. Moore took the case all the way to the US Supreme Court, which ruled that the Georgia legislature had infringed upon Bond’s First Amendment rights. Moore also successfully defended Stokely Carmichael, another SNCC member and the originator of the phrase “Black Power,” against charges of insurrection resulting from a 1966 riot in Atlanta’s Summerhill neighborhood. Much as Angela Davis would argue later, Carmichael claimed that the state had embraced a flimsy pretext in order to silence his political activity. As legal historian Tomiko Brown-Nagin – who wrote about both the Bond and Carmichael cases in her book on the civil rights struggle in Atlanta – has noted, these victories earned Moore a reputation as “a ‘splendid’ go-to lawyer for peaceniks and leftist radicals caught up in the clutches” of the ascendant and sometimes authoritarian American right. Indeed, after these cases, Moore defended a number of other dissidents against the Vietnam War, including several Atlantans who had refused draft induction.