The new bar is being built at 120 E. Franklin St., the former site of the X.O. South clothing store.
Employees say they hope to have the bar up and running in two or three weeks.
Manager Alex Louis, whose father, Mike Louis, owns the bar, said The Library will be different than other local bars because it's specifically designed as a venue for live music.
"We're trying to bring some live music to this side of Franklin Street," he said.
The Library will start hosting small, mostly local musical acts, Alex Louis said. "We're going to start off small and create a name for ourselves so people will want to come play here," he said.
Head bartender Andrew Tsui said the bar's management wants to offer live music because many local music venues are either on West Franklin Street or in Carrboro. "Hopefully, it's going to be a viable music scene in downtown Chapel Hill," he said.
The Library will have a small stage and public address system. Louis said the bar also will book some comedy acts and other performers.
"The Library will be the only bar on East Franklin with live music and a beautiful bar," Tsui said. "The bar will feature different kinds of music, depending on what day it is and the kind of atmosphere the staff is trying to create."
Tsui also said the bar will offer free food and said that although it features live music, it will not have a dance club atmosphere. "It's going to be a place you can dance, but it's not a dance club," he said.