Dorchester was platted in 1870 when the Burlington and Missouri River Railroad was extended to that point. The name was probably chosen to conform with the alphabetical stops on the new Burlington & Quincy Railroad line traveling westward from Lincoln: Berks, Crete, Dorchester, Exeter, Fairmont, Grafton, Huxley, etc. It was likely named after Dorchester, Massachusetts, although some say it was named for Dorchester, in England, which in any case is the namesake of the Massachusetts city. A 1925 edition is available for download at University of Nebraska—Lincoln Digital Commons.
