WASHINGTON — A Supreme Court term that is starting with a lack of headline-grabbing cases may end with a blockbuster that helps define the legacy of the court under Chief Justice John Roberts.

While same-sex marriage is not yet on their agenda, the justices appear likely to take on the issue and decide once and for all whether gay and lesbian couples have a constitutional right to marry.

When the justices formally open their new term Monday, Roberts will be beginning his 10th year at the head of the court, and the fifth with the same lineup of justices. He has been part of a five-justice conservative majority that has rolled back campaign finance limits, upheld abortion restrictions and generally been skeptical of the consideration of race in public life.

But his court has taken a different path in cases involving gay and lesbian Americans, despite his opposition most of the time.

The court’s record on gay rights is comparable to its embrace of civil rights for African-Americans in the 1950s and 1960s under Chief Justice Earl Warren, said University of Chicago law professor David Strauss. “The court will go down in history as one that was on the frontiers of establishing rights for gays and lesbians,” Strauss said.