"The court did not decide today whether those preferences are valid, but they seem one step closer to agreeing with the countless parents who simply want their children to be evaluated on the basis of their character and hard work," she added.
The case was brought by Fisher, a white Texan who says she was denied admission to the school in 2008 based on the color of her skin.
The Texas legislature passed the "Top Ten Percent Law" in 1997, which mandates that Texas high school seniors in the top 10 percent of their class be automatically admitted to any Texas state university.
In addition to that program, the school considers race and several other factors for admission. Fisher did not qualify for automatic admission.
Instead, she competed with other non-Top 10 state applicants, some of whom were entitled to racial preferences. She argues she was denied a fair chance at admission because of her race.
In briefs filed with the court, her lawyers argued, "the Fourteenth Amendment requires an admissions process untainted by racial preferences absent a compelling, otherwise unsatisfied, government interest and narrow tailoring to advance that interest without undue infringement on the rights of non-preferred applicants."
Fisher eventually attended Louisiana State University and is now working as a financial analyst in Austin, Texas.
Lawyers for the school argued that UT seeks to "assemble a class that is diverse in innumerable ways -- including race -- at advance its mission of educating students and preparing them to be leaders of tomorrow."
It was only in 2003 that the Supreme Court took up a similar affirmative action case and narrowly upheld the limited use of race as a factor in law school admissions. That decision, called Grutter v. Bollinger, held that the government has a compelling interest in diversity in public universities.
But after O'Connor retired, she was replaced with Justice Samuel Alito, who is more skeptical of racial classifications.