Astead: South Carolina, which votes fourth in the Democratic primary and is particularly important because of its high percentage of black voters, has played host to several likely presidential hopefuls in recent days, including Ms. Harris’s Senate colleagues Cory Booker of New Jersey and Bernie Sanders of Vermont.

The difference for Ms. Harris? She has been able to lean on her enormous network as a member of Alpha Kappa Alpha Sorority Inc., the country’s oldest black sorority. On Friday, she was the noted guest at the group’s annual Pink Ice Gala, which afforded her an audience of thousands of black South Carolinians at the ticketed event.

“I’m so honored to celebrate with my sorors,” she said. “We stand on the shoulders of women who were leaders, who 111 years ago said to us that we must honor sisterhood and service.”

The room was a preview of the electorate that could help slingshot her to victory. Older black residents, all dressed in black tie for the event, rushed the stage to get a photo with the presidential candidate, or to stream her speech on their social media channels. Ms. Harris did not mention her presidential candidacy in the short remarks, but the crowd knew this was the beginning of a long-term courtship.

In a short gathering with reporters after, Ms. Harris said it was important to her to attend the event, to highlight the importance of black voters — and particularly black female voters — but also to share how much the sorority means to her.