NEW YORK (AP) _ If her father wins the presidential election in November, 12-year-old Chelsea Clinton will be the first child in the White House since Amy Carter. Sometimes her parents worry about it.

Bill and Hillary Clinton's daughter has been in the background for most of the primary season, but her arrival here for the Democratic National Convention has placed the shy youngster squarely in the spotlight.

Clinton campaign aides have put her on a written schedule. And when she got leg cramps while walking up the stairs in the Statue of Liberty on Tuesday, security agents whisked her back to her hotel in a wheelchair.

They said later she actually needed no assistance.

When Chelsea arrived here for convention week, she had a new, more grown up look. Braces remained on her teeth but she wore a short skirt, in marked contrast to the childish looking dresses she favored until a week ago.

She held onto her mother's hand and practiced a still tentative campaign wave.

''It's an overwhelming experience for a child,'' said Hillary Clinton in between campaign stops this week.

''But she's a great kid and she's doing fine,'' her mother added.

Mrs. Clinton said her separations from Chelsea have been ''the hardest part of the campaign.''

''I've tried very hard over the last few months to rearrange our schedules so we'd both stay involved in our parenting lives,'' Mrs. Clinton said. ''But we've all still had to make adjustments. Chelsea included. Fortunately, we have a lot of friends and family who help out.''

Chelsea has been to the Hard Rock Cafe and to the musical ''Phantom of the Opera'' while in New York. Larry Trice, a Little Rock attorney and family friend, said Tuesday that Chelsea returned from the play, ''hit the door of the suite, gave her momma a hug and jumped on (her father's) lap'' where she remained to watch the opening night of the convention.

Chelsea's parents do not permit interviews. But she must be smart.

The eighth grader named for the song ''Chelsea Morning'' has already skipped one grade at her public school in Little Rock.

She also plays volleyball and softball and studies ballet.

Clinton said last week that he and his wife ''are committed to preserve Chelsea's childhood, to giving her the richest and most normal life we can.''

But in July 1991, he sounded less optimistic, saying ''if lightning should strike and I win, she loses me.'' Asked last week about that statement, Clinton quickly softened it.

''I was worried about her losing her childhood and her access to her parents,'' he said.

Linda Bloodworth-Thomason, co-producer of TV's ''Designing Women'' and ''Evening Shade'' and a longtime family friend from Arkansas says that ''Chelsea's a terrific, level kid.''

''She's a tribute to how they've raised her,'' Bloodworth-Thomason says.

Mrs. Clinton said she and her husband had hoped to go sightseeing with their daughter during convention week. But she grimaced over her packed schedule.

''We were hoping to have more time to spend with her but it's not working out that way,'' she said. ''We'll do what we can.''