A Career chip is an implanted electronic device which denotes what job someone is required to do. 30th century citizens are analyzed for their particular suitability for a career path and chips are implanted into their hands. These chips can be scanned and the job information is displayed.
Professor Hubert J. Farnsworth replaced the entire Planet Express crew's career chips with the chips of the old crew from a package labeled "Contents of Space Wasp's Stomach", A foreshadowing of a much later episode The Sting.
Fry and Leela's roles were reversed in The Cryonic Woman when their chips were mixed up. Fry became a cryogenics worker and Leela was forced to take up his career-chip mandated job as a delivery person.
The machine used to implant these is similar to a hammer, in that it performs a function, though the back has a part that can reverse the function. It is shown that implanting and removing a career chip is a very painful procedure.
They were only mentioned twice in the series, becoming defunct plot devices as later episodes show people applying for job normally. Basically, they fell in the throw away gag department.