The last dry town on the Vineyard could be turning wet.

The Chilmark selectmen have set a public hearing for August 27 to explore the idea of allowing alcohol sales at restaurants in the up-Island town. The move comes after selectmen received a request from the owners of the Beach Plum Inn and Home Port restaurants to bring liquor licenses to their establishments.

“We are looking to enhance the Home Port Restaurant and the Beach Plum Inn and Restaurant by providing our guests the ability to purchase alcohol directly from the restaurants,” owners Bob and Sarah Nixon wrote in an August 5 letter.

“We would like to assist the town, in any way that we can, in working towards alcoholic liquor licenses for Chilmark.”

Still in the early stages, the public hearing is meant to “generate discussion and find out whether it’s important to people in town,” selectman Bill Rossi said at the board’s weekly meeting on Tuesday. “This is a big issue.”

In order for liquor licenses to be distributed, the town would have to file a home rule petition with the state legislature seeking the right to place a question on the ballot at the annual town election. A move to file the petition could be done as soon as a special town meeting scheduled for Sept. 30, executive secretary Tim Carroll said.

Selectman Warren Doty said he wanted to hear more from Chilmarkers.

“I have not heard enough interest from the citizens of the town of Chilmark in changing our liquor law,” he said. “I need to know if this is an issue of importance to the people of my town. I haven’t heard anybody say that.”

The Beach Plum, Home Port and Chilmark Tavern are the only large sit-down restaurants in Chilmark.

West Tisbury was the most recent Island town to approve the sale of beer and wine, in 2011. Chilmark and Gosnold are the last dry towns in Dukes County.