Eastham was born about 1828, the son of David Eastham, a slaveholding farmer, and Elizabeth Bunch Eastham. Keepers of public records sometimes rendered the family name as Estham or Esom, which suggests the possible pronunciation. By August 1850 Eastham was practicing medicine in his native Louisa County. He inherited two tracts of land totaling almost eighty-two acres from his maternal grandfather, but in 1849 he sold this property to his father for $350 and continued to live in his parents’ household. On October 12, 1858, Eastham married Anna E. Pettus, also of Louisa County. They had one daughter and four sons, one of them born after Eastham’s death. In 1860 he, his wife, and a medical student whom Eastham was training were boarding with a prosperous farmer. That year Eastham owned one female slave, and at other times he, one of whom ran away while in his employment.
Eastham was a Unionist during the Civil War and by 1867 had joined a Union League. During the spring of that year he signed a circular letter, penned by the moderate Republican John Minor Botts, declaring himself an “unconditional Union” man and a member of “the great ‘Republican Union party‘” and urging like-minded citizens to organize themselves to influence the autumn election. Describing Eastham in March 1867 as “a good and true man of strong Union sentiment,” the district superintendent of the Bureau of Refugees, Freedmen, and Abandoned Lands recommended him as one of six prominent and influential Louisa County white men eligible to hold office under Reconstruction. On October 22 of that year Eastham won election to represent Louisa County in the constitutional convention called in compliance with federal Reconstruction legislation.
Eastham received 1,592 ballots from African Americans, who were voting for the first time, and 72 from white men, while the Conservative candidate, a former Confederate captain, garnered 541 white votes and only 3 black ones. Three days after his victory at the polls Eastham tendered his resignation, explaining in the Richmond Daily Whig that he was a compromise candidate and that his election was not satisfactory to all party members. The commander of therefused to accept Eastham’s resignation, however, on the grounds that he had no authority to do so and that Eastham had willingly sought the seat.
At the convention, which met in Richmond from December 3, 1867, to April 17, 1868, Eastham held low-ranking seats on the Committees on Education and the Funds Relating Thereto and on Future Revision and Amendment of the Constitution. He missed or abstained from many key votes and made no formal remarks during the portion of the convention for which a record of debates survives. Characterized as a moderate Republican, Eastham declared that he came to the convention ready to compromise on issues in the interest of restoring harmony. He supported enfranchising African American men but voted with Conservatives on issues involving restrictions on voting or officeholding by former Confederates. He opposed disfranchising whites who had cast ballots for secessionist candidates to theand also the imposition of a test oath that would have prevented many whites from holding elective office. Eastham backed efforts to require racial segregation in the new . On April 17, 1868, he joined twenty-five other delegates in voting against the final version of the constitution. In explaining his opposition, Eastham denounced the acrimonious debates indulged in by delegates who had placed personal and party interests above reconciling the state’s hostile factions and likened them to the unnatural mother who was willing to have King Solomon split in twain the baby she falsely claimed was hers. He urged Virginians to reject ratification of a document he considered divisive and as violating “both the letter and spirit” of Congress’s Reconstruction acts.
Eastham died of hepatitis on an unrecorded date in July 1869. Most likely he was buried in the Pettus family cemetery near Bumpass, where at least two of his children have grave markers.