A while back someone put every issue of OMNI Magazine online for free download in PDF and other formats. Over at the William Gibson forums, Memetic Engineer rounded up all the issues of OMNI that are available for download and have stories by William Gibson in them:
May 1981, features “Johnny Mnemonic.” From the contributors page: “Gibson is a full-time writer living in Vancouver, British Columbia. His work appears in two anthologies, Universe 11 and Shadows 4, both published this year by Doubleday. The issue also features a story by Ray Bradbury and an interview with David Cronenberg.
July 1982 features “Burning Chrome.”
July 1983 features “Red Star, Winter Orbit” by Gibson and Bruce Sterling.
July 1984 features “New Rose Hotel.” (Which was turned into the Gibson movie you never heard about: directed by Abel Ferrara and starring Christopher Walken, Willem Dafoe and Asia Argento)
July 1985 features “Dogfight” by Gibson and Michael Swanwick.
The October 1981 issue features “Hinterlands,” but it’s not available in the OMNI archives.
The text on these scans is readable but blurry. If you just want to read the stories, buy the Burning Chrome collection.
See also: William Gibson dossier