We report the first results from the Z -FOURGE survey: the discovery of a candidate galaxy cluster at z = 2.2 consisting of two compact overdensities with red galaxies detected at ≳ 20σ above the mean surface density. The discovery was made possible by a new deep (Ks ≲ 24.8 AB 5σ) Magellan/FOURSTAR near-IR imaging survey with five custom medium-bandwidth filters. The filters pinpoint the location of the Balmer/4000 break in evolved stellar populations at 1.5 < z < 3.5, yielding significantly more accurate photometric redshifts than possible with broadband imaging alone. The overdensities are within 1′ of each other in the COSMOS field and appear to be embedded in a larger structure that contains at least one additional overdensity (10σ). Considering the global properties of the overdensities, the z = 2.2 system appears to be the most distant example of a galaxy cluster with a population of red galaxies. A comparison to a large ΛCDM simulation suggests that the system may consist of merging subclusters, with properties in between those of z > 2 protoclusters with more diffuse distributions of blue galaxies and the lower-redshift galaxy clusters with prominent red sequences. The structure is completely absent in public optical catalogs in COSMOS and only weakly visible in a shallower near-IR survey. The discovery showcases the potential of deep near-IR surveys with medium-band filters to advance the understanding of environment and galaxy evolution at z > 1.5.