The ballot initiative, which passed with 52 percent of the vote in November, took away the right for gay couples to marry. Spending for and against the amendment reached $74 million, making it the most expensive and arguably the most high profile of the nation's 153 ballot measures in last fall's election.
The ballot's passage overrode last year's 4-3 state Supreme Court decision that held that denying same-sex couples the right to wed was a civil rights violation.
NewsHour correspondent Spencer Michels attended Thursday's hearing. Listen to him describe the scene outside the courthouse, recap the day's arguments and give background on the state's same-sex marriage debate:
Gay-rights groups, a group of local governments and others are urging the court to overturn the measure on the grounds that it was put before voters improperly.
Under state law, the Legislature must approve significant constitutional changes before they can go on the ballot.
The measure's sponsors, however, argue the ballot initiative was approved fairly and it would be a miscarriage of justice for the court to overturn the results of a fair election.
Fewer than two dozen people, who waited in line early Thursday, were able to get seats in the courtroom for the three-hour hearing, the AP reported.
Hundreds of others demonstrated outside the courthouse and watched the proceedings on a large television screen.
Outside the court, supporters of gay marriage carried rallied in support the overturning the ban, which took away the right of gay men and lesbians to wed and threw the legality of thousands of previous same-sex unions into question.
Nearby, opponents of the unions held signs left over from last year's campaign that said "Yes on 8." Others said, "A moral wrong cannot be a civil right," according to the AP.
Will Prop. 8 Ruling Lead Supreme Court to Consider Same-Sex Marriage?
