When it comes to vaccinating its residents, Northeast Tennessee counties are leading the way in Tennessee. Of the six counties with the highest percentage of its population partially vaccinated, Northeast Tennessee had three as of Tuesday â Hancock (5.92%), Unicoi (5.05%) and Washington (4.41%) counties. Hancock Countyâs rate is tied with that of Carroll County for the highest rate in the state, while Unicoi Countyâs rate is third. Overall, the regionâs eight counties have combined to administer 17,993 vaccinations, about 10.6% of the stateâs total. Washington County has inoculated the most people with 6,162 vaccines administered as of Jan. 4, followed by Sullivan Countyâs 4,763. Carter (1,635), Greene (1,910) and Hawkins (1,733) have also vaccinated at least 1,000 people. Approximately 3.5% of the regionâs population has been vaccinated.