A roller chain for bicycles having outer and inner chain links. The outer and inner chain links have outer and inner link plates, respectively. The chain links are joined by tubular pins. The chain links have holes for receiving the tubular pins. The holes have an outward-opening conical contour for receiving a deformed head of the pin. The roller chain is assembled into a working unit by using a closing link to join two inner chain links. The closing link can be assembled and dismantled without plastic deformation or press-fitting forces on the closing link. The configuration of the hole contour and deformed heads allows the outer link plates to enter into a connection with the pins such that a slight movement of the pin in its seat in the hole in the outer link plate.