We present a dynamical study of the Cl 0023+0423 system at a redshift of z = 0.84. This system consists of two components separated in velocity space by ~2900 km s-1 and on the plane of the sky by ~0.23 h-1 Mpc. A kinematic analysis indicates that the two components are a poor cluster with a velocity dispersion of 415 km s-1 and a mass of ~3?6 ? 1014 h-1 M?, and a less massive group with a velocity dispersion of 158 km s-1 and a mass of ~1013 h-1 M?. The dynamics of galaxy groups at high redshift can provide important insights into the creation of present-day galaxy clusters. Therefore, we have performed a dynamical study on this system in order to determine whether the two groups are infalling. This analysis includes an analytic two-body calculation and N-body simulations. The results of both studies indicate that the system is most likely not bound, but simply a chance projection on the sky; however, within the observational uncertainties, there exist bound solutions where the two galaxy groups are currently moving toward each other and will eventually merge into a larger system of galaxies. We have run 1000 N-body simulations with random initial conditions based on the observed parameters of the Cl 0023+0423 groups. A statistical analysis of these simulations indicates that there is a 20% chance that the two groups will merge. If the Cl 0023+0423 system does merge, it will appear as a cluster on the sky, as well as in velocity space, within 1?2 Gyr. The cluster will evolve dynamically for more than 3 Gyr, appearing during this time more similar to an open, irregular cluster. The final merged system has a velocity dispersion that is consistent with a local Abell richness class 1 cluster. The morphological analysis of the galaxy populations of Cl 0023+0423 suggests that both groups are largely dominated by spiral galaxies. Early-type fractions are 33% or less. These modest early-type fractions have implications for both cluster formation and group evolution. Studies of open clusters at z = 0.31?0.54 indicate that they have early-type fractions between 45%?80%. If the Cl 0023+0423 system is the predecessor of such a cluster, the comparison may suggest that some fraction of early-type galaxies are formed between redshifts of z ~ 0.8 and z ~ 0.3; however, the morphological fractions are still highly uncertain. In addition, the modest early-type fractions in both groups may be inconsistent with the strong correlation between velocity dispersion and early-type fraction observed in nearby groups of galaxies. Both groups apparently have relatively low early-type populations, irrespective of their velocity dispersion. If the groups of Cl 0023+0423 are typical of galaxy groups at high redshift, and if high-redshift groups are the progenitors of local groups, this result may also imply that some early-type formation is occurring at redshifts of z 0.8. These results do not preclude the formation of early-type galaxies at very high redshift, as many observations suggest; however, the observations of the Cl 0023+0423 system may imply that a fraction of the early-type population is forming and/or undergoing significant evolution at redshifts of z < 1.