Tesla's online job board currently has a post for an Advanced Driver Assistance Systems Controls Engineer, who will be responsible for helping "Tesla's effort to pioneer fully automated driving."
On top of the technical obstacles, legal and safety issues must be overcome before driverless cars are allowed on the road.
European Union laws currently call for drivers to control their cars at all times.
And it is unclear whether the multibillion-dollar car insurance industry has any appetite to back the cars until the technology is proven, although driverless cars would be free from human error and programmed to obey traffic laws, features that could appeal to insurers.
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Buyers may also be skittish about purchasing a car that drives itself until its safety has been proved through real world experience.
Musk's three-year timeline is more ambitious than timelines set out by other carmakers, as well as analysts that say it will take 10 to 15 years before self-driving cars become a reality.
Germany's Daimler and Japan's Nissan have both said they hope to begin selling self-driving cars by the end of the decade.
Daimler already offers technology that allows for partly automated driving such as traffic jam assistance in its top-line S-Class Mercedes, which can maintain distance to other cars in stop-and-go situations.
Google has fitted out several cars with radar-like equipment that lets them navigate roads in California and Nevada. Google did not immediately respond to an inquiry about the status of its driverless car program.
California Governor Jerry Brown signed a law last year allowing the Mountain View-based internet giant to test its self-driving cars on the road.