Using a sample of 299 H{alpha}-selected galaxies at z~~0.8, we study the relationship between galaxy stellar mass, gas-phase metallicity, and star formation rate (SFR), and compare to previous results. We use deep optical spectra obtained with the IMACS spectrograph at the Magellan telescope to measure strong oxygen lines. We combine these spectra and metallicities with (1) rest-frame UV-to-optical imaging, which allows us to determine stellar masses and dust attenuation corrections, and (2) H{alpha} narrowband imaging, which provides a robust measurement of the instantaneous SFR. Our sample spans stellar masses of ~10^9^-6x10^11^M_{sun}_, SFRs of 0.4-270M_{sun}_/yr, and metal abundances of 12+log(O/H)~~8.3-9.1(~~0.4-2.6Z_{sun}_). The correlations that we find between the H{alpha}-based SFR and stellar mass (i.e., the star-forming "main sequence") and between the stellar mass and metallicity are both consistent with previous z~1 studies of star-forming galaxies. We then study the relationship between the three properties using various plane-fitting techniques and a curve-fitting projection. In all cases, we exclude strong dependence of the M_{star}_-Z relation on SFR, but are unable to distinguish between moderate and no dependence. Our results are consistent with previous mass-metallicity-SFR studies. We check whether data set limitations may obscure a strong dependence on the SFR by using mock samples drawn from the Sloan Digital Sky Survey. These experiments reveal that the adopted signal-to-noise ratio cuts may have a significant effect on the measured dependence. Further work is needed to investigate these results, and to test whether a "fundamental metallicity relation" or a "fundamental plane" describes star-forming galaxies across cosmic time.