We present a detailed gravitational lens model of the galaxy cluster RCS2 J232727.6-020437. Due to cosmological dimming of cluster members and ICL, its high redshift (z=0.6986) makes it ideal for studying background galaxies. Using new ACS and WFC3/IR HST data, we identify 16 multiple images. From MOSFIRE follow up, we identify a strong emission line in the spectrum of one multiple image, likely confirming the redshift of that system to z=2.083. With a highly magnified (\mu\gtrsim2) source plane area of \sim0.7 arcmin^2 at z=7, RCS2 J232727.6-020437 has a lensing efficiency comparable to the Hubble Frontier Fields clusters. We discover four highly magnified z\sim7 candidate Lyman-break galaxies behind the cluster, one of which may be multiply-imaged. Correcting for magnification, we find that all four galaxies are fainter than 0.5 L_{\star}. One candidate is detected at {>10\sigma} in both Spitzer/IRAC [3.6] and [4.5] channels. A spectroscopic follow-up with MOSFIRE does not result in the detection of the Lyman-alpha emission line from any of the four candidates. From the MOSFIRE spectra we place median upper limits on the Lyman-alpha flux of 5-14 \times 10^{-19}\, \mathrm{erg \,\, s^{-1} cm^{-2}} (5\sigma). Show Partial Abstract