A LARGE number of movie theaters around the country are planning to get serious about enforcing their restrictions on who's allowed to see R-rated films. The National Association of Theatre Owners, representing nearly two-thirds of the movie houses (more than 20,000 in all), announced this week that for motion pictures containing explicit violence or sex scenes, it will require photo IDs from young people who are unaccompanied by an adult, to prove they're 17 or older. The theater owners would like to avert any legislation restricting their marketing to young people. President Clinton said the plan will help "prevent youth violence" and "give our children the childhoods they deserve."

That's a fairly tall order for the nation's usher corps, which often has more immediate worries about popcorn sales, spilled drinks and people sneaking in the exit doors. And as might be expected, the new policy was met with a chorus of hoots from numerous under-age moviegoers, who made it clear they'll find ways to continue to see R-rated films. A good many probably will. Multiplexes make it hard to track who goes to what movie; fake IDs are a growing industry; many theaters will no doubt continue to wink at suspect young customers because they want their money.

But like most remedies aimed at a problem as complex as youth violence, this one will do some good. It isn't likely to keep the most violence-prone kids from seeing these films one way or another, and it's questionable how many serious incidents will be prevented by this kind of restriction. But a good number of the country's young people are likely to be deterred -- enough perhaps to prod Hollywood into producing more films that don't rely almost exclusively on gratuitous violence, sex and profanity occurring on a scale that bears little relation to the human condition or to anything that's been seen before in the long history of drama. The theater owners' plan is voluntary, which is much preferable to government's getting involved, and while it may not go that far in providing our children the childhoods they deserve, it might at least provide us all some better movies.