A drive-on system for installing a tire chain (i.e., snow chain) on a pneumatic tire mounted on a vehicle wheel. The system includes a U-shaped installation tool whose arms releasably engage fastening elements (hooks or links) at one end of each side chain, and a installation tray or ramp in which the connected tire chain and tool are arranged, and may be stored, prior to installation, with the tire chain in a partially laid-out orientation and the tool preferably within a tool compartment in the tray. To install the tire chain, the vehicle is driven onto the tray and stopped, preferably in a predetermined optimum position in response to a signal initiated by a position-indicating switch on the tray. Then the tool, with one end of the tire chain connected to it and trailing it, is drawn upward and circumferentially around the tire. With the tool bridging the tread of the tire so that its arms extend along the opposite sidewalls, the tire chain is draped and tensioned substantially in the correct position on the tire. The fastening element at the other, free end of each side chain is then removed from its place in the tray and connected to the mating fastening element. The connection on the inner sidewall is preferably made while the tool is still connected, which enables the arm of the tool on the inner sidewall to be used to guide the free element into contact and connection with the element connected to the tool.