Chapman was elected to the New South Wales Parliament as the Liberal Party member for [Electoral district of Electoral district of Nepean (New South Wales)|Nepean (New South Wales)|Nepean] in 1956. The sitting Liberal member Joseph Jackson had retired and Chapman defeated Jim Chalmers, the Independent Labor member for Hartley, who attempted to transfer to Nepean. Chapman retained the seat at the 1959 election. He was defeated by Labor's Alfred Bennett in 1962 after an unfavourable redistribution made Nepean a notionally Labor seat. He failed to gain Liberal Party endorsement for the 1965 election and left the party in 1966. He did not hold a ministerial, party or parliamentary position.