Chichester studied filmmaking at New York University, which led to an editorial job at the Marvel Comics imprint Epic Comics. Working as an assistant editor from 1985—1986, he was promoted to associate editor in 1987. In 1989, Chichester was made a full editor, and he worked in that capacity at Epic until 1996.

Beginning in 1990, Chichester started writing for comics, for Marvel and for freelance clients. His credits include a long run on Daredevil from 1991—1995, where he scripted the "Fall From Grace" story arc; he also worked on Agent of S.H.I.E.L.D. from 1990—1992, and Nightstalkers from 1992—1993. Freelance credits from this period include Charlemagne #1—5 for Defiant Comics, and Motorhead #1—6 for Dark Horse Comics.

Chichester's departure from Marvel's staff in 1996 was precipitated by a conflict over his work as Daredevil writer in 1995. Chichester learned during a brief break from the series that he was to be replaced; for the five issues he was obligated to write he took his name off the credits, instead demanding an "Alan Smithee" credit. Despite this unpleasant ending to his regular writing career, Chichester was given the opportunity to write the 1997 Daredevil/Batman intercompany crossover, "An Eye for an Eye."

Chichester has had no major comics writing credits since 1999, the same year he joined the ad agency Ogilvy & Mather as an associate creative director. He is currently a creative director at the company.

He lives in his native Connecticut with his wife and son, continuing to experiment with moviemaking and animation.