Costa has been in the family restaurant business since the age of eight when his career began as Assistant Dishwasher. He rose quickly (usually standing on top of a milk crate) to Assistant manager and Chef while apprenticing in his father's California restaurant. Costa received his formal education at Utah State and The University of Denver in their hotel and restaurant management program.
In 1986, Costa and his father opened the Greek Bistro in Maui, Hawaii. In 1990, Costa moved to Dallas and opened the Greek Bistro on lowest Greenville. After selling the M Street Bistro to friend Teiichi Sakurai, owner of Teppo, Yakitori & Sushi Bar, he opened Ziziki's, in Travis Walk, in July, 1994 with his wife and partner, Mary Cloutier-Arabatzis. Costa's family recipes of his Greek grandmother and father and Italian mother are recreated at Ziziki's with a more gourmet flair.

In December 1999, Costa and Mary combined their talents and opened a second Ziziki's at the Shops of Spanish Village in North Dallas.

"A lot of people say the restaurant business is tough. I think it's tough only if you don't make a product that's outstanding. It's like that in any business and particularly in the restaurant business where our best form of advertising and promotion is positive word of mouth from loyal customers."

"We don't do a lot of specials at Ziziki's, usually only one each night. We believe it is more important to put the time and energy into making everything on the menu special. Our goal is to make every plate on the menu the kind of unique, fabulous flavor and presentation that our chefs, wait-staff and customers feel is the very best and will want to eat every day." - Costa Arabatzis