Definitely replace it. No need to have it come off again while driving, sending shrapnel through the engine!
There is a band of rubber sandwiched under that outer ring. The purpose of that ring is to dampen out crankshaft oscillations. In real severe conditions, such as very high rpm and load, the crankshaft can twist and bend slightly resulting in a broken crank. More importantly, many engines are " externally balanced" meaning that when they were cast, it was very difficult to cast in two of the counterbalance weights, so they put them on the harmonic balancer and on the torque converter or flywheel. If the ring is not in the correct position on the hub, severe engine vibration will result. You might not actually feel the vibration, but the crankshaft will sure feel it.
Ford has a lot of trouble with the outer ring shifting position resulting in running problems because they include a position sensor in it. With Chrysler vehicles, the most common cause of the ring coming off is incorrect removal tools and procedures. The damper puller must be threaded into the holes designed for the purpose. If a jaw-type puller is used, the jaws must pull on the center hub, never on the outer ring.
A large selection of replacement dampers are available at some of the parts stores, otherwise you can find them at the local salvage yard. Be sure to find one from the same engine size and model year.