We present the Team Keck Redshift Survey 2 (TKRS2), a near-infrared spectral observing program targeting selected galaxies within the CANDELS subsection of the GOODS-North Field. The TKRS2 program exploits the unique capabilities of MOSFIRE, an infrared multi-object spectrometer which entered service on the Keck I telescope in 2012 and contributes substantially to the study of galaxy spectral features at redshifts inaccessible to optical spectrographs. The TKRS2 project targets 97 galaxies drawn from samples that include z~2 emission-line galaxies with features observable in the JHK bands as well as lower-redshift targets with features in the Y band. We present a detailed measurement of MOSFIREs sensitivity as a function of wavelength, including the effects of telluric features across the YJHK filters. The largest utility of our survey is in providing rest-frame-optical emission lines for z>1 galaxies, and we demonstrate that the ratios of strong, optical emission lines of z~2 galaxies suggest the presence of either higher N/O abundances than are found in z~0 galaxies or low-metallicity gas ionized by an active galactic nucleus. We have released all TKRS2 data products into the public domain to allow researchers access to representative raw and reduced MOSFIRE spectra.