We examine the possibility of using rare, three-body decays of a new neutral gauge boson Z , to probe its gauge couplings at hadron colliders. Specifically, we study the decays Z , + W l v and Z , +ZvG and find that much knowledge of the Z , properties can be obtained from these processes. In particular, these decay modes can yield valuable information on the amount of Z 1 -Z , mixing, on the generation dependence of the Z , couplings, and on the properties of the new generator associated with the Z , , as well as being used to distinguish between possible extended models. Standard model backgrounds to these three-body decays are discussed, and we find that the rate for pp+ZZ+ZvV eclipses that of pp+Z,+ZvV at hadron supercolliders. The analogous three-body decays into a new, heavy charged gauge boson, Z , + ~$ 1 v, are also investigated in models where this can occur. PACS numberk): 13.38.+c, 12.15.C~ It is now commonly accepted that if a new neutral gauge boson ( Z ' ) exists, it should be observed by direct production, via pp -z'-1 + 1 -, at both the Superconducting Super Collider (SSC) and CERN Large Hadron Collider (LHC) if its mass is of order a few TeV or less [I](provided it couples to both qq and 1 + 1 -pairs at or near electroweak strength). Indeed, if a Z' is discovered we will want to learn as much about it as possible; in particular, the next logical step would be to determine its gauge couplings and the extended model from which it originates. Unlike e + e -machines. hadron colliders are limited to only a few measurable quantities with which the new gauge boson properties can be determined. In addition to obtaining the Z' mass, the planned SSC and L H C detectors [2] will be able to collect data on the Z' production cross section and subsequent decay into 1 +1-, the full Z' width, and the leptonic forward-backward asymmetry. Unfortunately, these measurements will not only be statistics limited but also will experience reasonably large systematic effects due to finite mass resolution and efficiencies as well as uncertainties in the collider luminosity. T o further extract coupling information, uncertainties in the parton distributions will also contribute to the systematic errors. If, however, several theoretical assumptions are made, one can use the above data to distinguish new Z' bosons from different models with reasonable reliability [3].In order to obtain more information on Z' couplings, we need an additional set of quantities, which do not suffer the large theoretical or systematic uncertainties discussed above, can be measured with reasonable statistics, and yet are sensitive to the particular extended model. Since decay modes involving leptons provide the cleanest signatures and the conventional 1+1-mode is already being used to discover the Z ' , one of the next possibilities to consider is various three-bodv decavs. One DOtential process [4], which has recently been revived in the literature [5], is to look for the decay Z'-W*l ' v, and, in particular, to measure the ratio which suffers ve...