His opponent is incumbent Lindsey Graham, a close Donald Trump ally and vocal cheerleader for the president.
If he beats Graham, South Carolina would become the first state with two sitting African American senators ever.
The South Carolina senator Tim Scott is one of the few African American senators in the chamber, and the only Black Republican.
There have been 1,974 members of the US senate since it was established in 1789 – only 10 have been Black.
South Carolina has emerged, surprisingly, as one of the best chances Democrats have to get the three or four seats needed to retake control of the Senate.
If Trump was to win the Presidency but Republicans lose control of the Senate it would severely limit the legislation that he could get passed.
A New York Times/Siena College poll of the race published on Thursday found Graham leading Harrison by six percentage points. »