The young woman was found lying in the road just before 6:30 a.m. Tuesday.
She was taken to the hospital with head injuries.
The driver kept going. Police don't have a description of the vehicle.
Neighbors found the incident disturbing.
"That's ridiculous. I feel like this is a pretty safe area, and I feel comfortable obviously looking where I am going, but crossing the street is not a problem here," said Anne Patterson, who lives downtown.
Police are offering cash to people who come forward with information that leads to an arrest. Callers can remain anonymous.
If you have any information, please call (919) 683-1200.