After beginning the 1989–90 season with Utica, Cichocki was traded to the Hartford Whalers for Jim Thomson on October 31, 1989. Cichocki was quickly placed on Hartford's farm team the Binghamton Whalers and again started to put up big numbers. In four seasons with the Binghamton Whalers (renamed the Binghamton Rangers in 1990), Cichocki chalked up 221 points, including three 50-point seasons and 18 points within three playoff runs, all of which ended in the semi-finals to division rival the Rochester Americans.