'Hopefully, soon everybody can get covered' | Publix begins vaccinating people in South Carolina As the state pushes to speed up the vaccination rollout, Harris Teeter also plans to start administering shots. Author: Chloe Leshner (WCNC) Updated: 6:14 PM EST January 20, 2021 YORK COUNTY, S.C. — In South Carolina, vaccine rollout remains sluggish. The state is vaccinating front line healthcare workers most at risk of being exposed to coronavirus, as well as people 70 and older. On Wednesday, Publix started administering some of those vaccines. Across the state, 42 locations got 100 doses each. It’s another way to make it easier to get as much vaccine as possible into people’s arms.