He studied law and admitted to the bar in 1854, practicing in the Lake Superior region.
He engaged in the Lake Superior region as explorer for the Montreal Mining Company in 1846 and was assistant clerk of the Michigan House of Representatives in 1853. Chipman returned to Detroit and was city attorney from 1857 to 1860. In 1866, he ran as the Democratic candidate for the United States House of Representatives from Michigan"s 1st congressional district, losing in the general election to Republican incumbent Fernando C. Beaman.
Attorney of the police board of Detroit from 1867 to 1879, Chipman was elected judge of the superior court of Detroit on May 1, 1879.
He was reelected in 1885 and served until he resigned in 1887. Elected as a Democrat in 1886 to the Fiftieth Congress and re-elected to the three succeeding Congresses, Chipman served as United States Representative for the first district of the state of Michigan from March 4, 1887, until his death.
Chipman died of pneumonia in Detroit, Wayne County, Michigan, on August 17, 1893 (age 63 years, 73 days). He is interred at Elmwood Cemetery, Detroit, Michigan.
In 1865 and 1866, he was a member of the Michigan House of Representatives representing the First District of Wayne County.