 Governor George C. Peery nominated Eggleston to the Supreme Court of Appeals, and fellow legislators elected him to that position in 1935.In 1958, Eggleston became chief justice and served in that position until he retired on September 30, 1969, and was replaced as justice by former state senator George M. Cochran of Staunton, Virginia and as Chief Justice by Harold Fleming Snead, who ironically had been one of only two dissenters from one of Eggleston's most important opinions as discussed below.Although Eggleston firmly believed in states' rights, he became best known for the opinions he wrote overturning attempts by Virginia legislators to avoid complying with the United States Supreme Court's decisions in "Brown v. Board of Education" (which had a companion case Davis v. County School Board of Prince Edward County).