Small restaurants in outer neighborhoods could soon be letting their customers bring a bottle of wine or some beer with them to enjoy with their meals.

On Monday, the Boston Licensing Board begins accepting applications for BYOB permits for restaurants with fewer than 30 seats that don't already have liquor licenses. The board will then schedule public hearings on the permit requests.

City officials hope BYOB will help out restaurants in a city where even a beer-and-wine license can go for $60,000 due to state-imposed quotas on licenses - and bring new life to neighborhoods not overrun by national chains that can afford the even more expensive full-liquor licenses. Restaurants downtown and in the North End, the South End, Bay Village, Fenway, Chinatown, the Seaport, the West End, Beacon Hill and Back Bay are not eligible.

Restaurants that win a BYOB permit will face a series of restrictions: Customers can't bring in more than a single 750-ml bottle of wine or 64-oz. container of beer - and can't go out during a meal to get more; new servers will have to undergo an alcohol training program; no spirits or liqueurs allowed; no corkage fees permitted; and restaurants can only offer BYOB between 5 p.m. and 11 p.m.

However, restaurants will be allowed to provide glassware and bottle openers to BYOBing customers.

The board approved the BYOB concept earlier this month - some two years after city councilors Michelle Wu and Steve Murphy first proposed it.