For Bo Muller-Moore, a folk artist from Vermont, the T-shirts he hand-screens with the slogan “Eat More Kale” are a dream fulfilled: a quirky project that has emblazoned this leafy mandate across the chests of people worldwide, and one he wants to trademark.

So when Chick-fil-A, the fast-food chain that says it sells 537 sandwiches a minute with the help of the slogan “Eat mor chikin” (the words have been penned by cows), sent him a cease-and-desist letter this fall, Mr. Muller-Moore decided to fight the company, setting off a groundswell of local support and national media attention.

“This is corporate bullying,” Mr. Muller-Moore said. His lawyer, Daniel Richardson, sent Chick-fil-A a letter in November, contesting its claim that the slogan “is likely to cause confusion of the public and dilutes the distinctiveness of Chick-fil-A’s intellectual property.”

Chick-fil-A does not have any stores in Vermont. The closest one is in Nashua, N.H., about 120 miles from Montpelier, where Mr. Muller-Moore, an Alabama native, has lived for years. He began making the shirts in 2000, at the suggestion of a local farmer. The few dozen printed at first have swollen into thousands of orders filled every year, he said, but he still works out of the overflowing studio above his garage, buying his art supplies nearby.