Hang on, I'll wiki...
On June 18, 2003, the Chapman trio captured convicted fugitive rapist Andrew Luster (heir to Max Factor cosmetics), who had fled to Mexico.
The program spun off from their appearance in the A&E Network's Take This Job, a program about people with unusual occupations. Both shows are produced for A&E by Hybrid Films, a New York-based production company.
the A&E cable series Take This Job [first aired in 2003]... revolved around unusual people in unusual professions. The opening episode set the series' tone by focusing on prominent Hawaiian bounty hunter Duane "Dog" Chapman, whose recent capture of millionaire fugitive Andrew Luster had made international headlines
[the "Dog the Bounty Hunter Show]
Original channel A&E Network
Original run August 30, 2004 Present
Looks like he made the capture, got the A&E segment later that year and then a year later got his own show. He was well-known in the bounty hunter community prior to the Luster bust (lust-or-bust, heh) but not a "star".