The high-frequency-peaked BL Lacertae object RGB J0710+591 was observed in
the very high-energy (VHE; E > 100 GeV) wave band by the VERITAS array of
atmospheric Cherenkov telescopes. The observations, taken between 2008 December
and 2009 March and totaling 22.1 hr, yield the discovery of VHE gamma rays from
the source. RGB J0710+591 is detected at a statistical significance of 5.5
standard deviations (5.5{\sigma}) above the background, corresponding to an
integral flux of (3.9 +/- 0.8) x 10-12 cm-2 s-1 (3% of the Crab Nebula's flux)
above 300 GeV. The observed spectrum can be fit by a power law from 0.31 to 4.6
TeV with a photon spectral index of 2.69 +/- 0.26stat +/- 0.20sys. These data
are complemented by contemporaneous multiwavelength data from the Fermi Large
Area Telescope, the Swift X-ray Telescope, the Swift Ultra-Violet and Optical
Telescope, and the Michigan-Dartmouth-MIT observatory. Modeling the broadband
spectral energy distribution (SED) with an equilibrium synchrotron self-Compton
model yields a good statistical fit to the data. The addition of an
external-Compton component to the model does not improve the fit nor brings the
system closer to equipartition. The combined Fermi and VERITAS data constrain
the properties of the high-energy emission component of the source over 4
orders of magnitude and give measurements of the rising and falling sections of
the SED