A 14-year-old Mattapan girl has been charged with setting fire to the front door of Chez Vous, a roller-skating rink in Dorchester that provides an oasis from gang violence, prosecutors said. Suffolk District Attorney Daniel F. Conley said about 120 people were inside the building when the girl shoved burning paper underneath the door on Saturday, sparking the fire. Rink employees put out the blaze with a fire extinguisher and no one was hurt, although damage is estimated at $3,000, Conley’s statement said. The teenager allegedly set the fire around 10 p.m. Saturday after being denied admittance to the rink.Todd Feathers can be reached at firstname.lastname@example.org. Follow him on Twitter at @ToddFeathers.