Is Boston big enough for two Milk Streets?

Celebrity chef Christopher Kimball in 2010.Suzanne Kreiter/Globe staff/File/Globe Staff

Boston could be too small for two Milk Streets — at least when it comes to food ventures with that name.

That’s what the founder of Milk Street Cafe is claiming in a trademark lawsuit filed in Boston federal court Wednesday against celebrity chef Christopher Kimball’s new business.

Kimball’s multimedia venture Milk Street Kitchen will focus on cooking classes at 177 Milk St. — several blocks from Milk Street Cafe’s location at 50 Milk St. — as well as a new public television cooking show and a magazine. Milk Street Cafe, meanwhile, is primarily a caterer, with a retail cafe.

But Milk Street Cafe founder Marc Epstein says the businesses are close enough in nature that he fears consumers will confuse the two and that his 35-year-old company will be overwhelmed by Kimball’s venture in online searches and social media references.

“The man has an international following,” said Epstein, who owns a majority stake in the cafe and catering business. “I can’t possibly compete with that. . . . The whole idea that I have to fight after 35 years for my name is insane.”

Kimball’s lawyer, Kenneth Plevan, maintains his client’s business is different enough from the Milk Street Cafe that consumers will not be confused. Plevan wrote a 14-page letter on June 14 to Epstein’s lawyer, Jennifer Furey, arguing that his client sees no reason the two names can’t “coexist in the same marketplace.”

Plevan argues that the Milk Street Cafe has no right to claim a monopoly on the name “Milk Street,” blocking other businesses on the street that aren’t in direct competition from using it.

Reached by phone on Wednesday afternoon, Plevan declined to comment.

The origins of this food fight can be traced back to last November. That’s when Kimball announced he would leave the Brookline-based corporate parent of cooking shows “America’s Test Kitchen” and “Cook’s Country,” as well as the Cook’s Illustrated and Cook’s Country magazines, following a management shake-up. He hosted both TV shows for years.

Epstein said he became concerned as soon as he learned about Kimball’s new venture, just over a month ago. His lawsuit seeks an injunction preventing Kimball from using the “Milk Street” name, an order transferring ownership of social media pages with that name to Milk Street Cafe, and unspecified financial damages.

“I tried really hard to take the high road and not get into the litigation side of this,” Epstein said. “We begged him, at this early stage before he’s opened anything, ‘Please change your name.’ ”

Within two weeks of the Milk Street Kitchen announcement, Epstein sent a personal letter to Kimball, inviting him to lunch and a tour of the kitchens at his catering business. The two met on June 10, according to the lawsuit. In response, Kimball’s lawyer sent the letter four days later explaining why Kimball won’t change the name.

“I love that he’s opening up in the neighborhood,” said Epstein, who employs about 75 full- and part-time workers at his business. “I wish him all the best. My one issue and only issue is that he’s taking our name.”

Epstein followed up with another letter, on June 29, again requesting the name change. In that letter, Epstein claims the confusion has begun, with people applying for jobs at Milk Street Cafe thinking it’s Kimball’s company. Customers have also asked if Kimball owns the cafe.

But Kimball’s side didn’t budge.

Furey, Epstein’s attorney, said it’s inevitable her client will lose revenue as Milk Street Kitchen’s marketing efforts eclipse Milk Street Cafe in Internet searches and on social media. The first issue of the Milk Street Kitchen magazine is scheduled to be available in late October, around the same time that the cooking classes will start. A pilot for Kimball’s new TV show is also scheduled to be shot in October, although it won’t air until September 2017, according to Milk Street Kitchen’s website.

“Milk Street [Cafe] is building its own unique identity . . . and it’s about to, overnight, lose complete control over the brand,” Furey said. “Mr. Epstein doesn’t want to be tied to a celebrity. . . . He’s built his own reputation, and he doesn’t want to be tied to somebody else’s reputation.”