Daniel Webster Chester was born in Noank, Connecticut on January 14, 1839 to Charles Chester and Betsy Wilbur. He was educated in the local schools, which he attended until about 13 years of age. As a young man he went to sea aboard the fishing smack Maria. During the first ten years of his career he was employed in the coasting trade with Southern ports and the West Indies aboard the two-masted schooner Triumph. During the next ten years he sailed to Australia, Africa, Europe, Peru, and the Philippine Islands. Chester served as master of the Dauntless from early in 1875 until she was driven ashore on the coast of Africa in the fall of 1883. Prior to serving aboard this ship, he was master of the schooner William C. Bee. He abandoned his seafaring life in 1883. After that he worked in the coal business.

On December 10, 1863 he married Mary Emma Fitch (1838-1918) and they had six children: Elizabeth D. "Lizzie" (1866-1875); Juliette F. (1869-1957); Hattie (1872-1873); John Debell Webster (1876-1916); Claude Milton (1878-1962); and John David (1880-1915).

On March 18, 1924 he died in Groton, Connecticut.