We report the observations of PG 1553+113 during the first similar to 200 days of Fermi Gamma-ray Space Telescope science operations, from 2008 August 4 to 2009 February 22 (MJD 54682.7-54884.2). This is the first detailed study of PG 1553+113 in the GeV gamma-ray regime and it allows us to fill a gap of three decades in energy in its spectral energy distribution (SED). We find PG 1553+113 to be a steady source with a hard spectrum that is best fit by a simple power law in the Fermi energy band. We combine the Fermi data with archival radio, optical, X-ray, and very high energy (VHE) gamma-ray data to model its broadband SED and find that a simple, one-zone synchrotron self-Compton model provides a reasonable fit. PG 1553+113 has the softest VHE spectrum of all sources detected in that regime and, out of those with significant detections across the Fermi energy bandpass so far, the hardest spectrum in that energy regime. Thus, it has the largest spectral break of any gamma-ray source studied to date, which could be due to the absorption of the intrinsic gamma-ray spectrum by the extragalactic background light (EBL). Assuming this to be the case, we selected a model with a low level of EBL and used it to absorb the power-law spectrum from PG 1553+113 measured with Fermi (200 MeV-157 GeV) to find the redshift, which gave the best fit to the measured VHE data (90 GeV-1.1 TeV) for this parameterization of the EBL. We show that this redshift can be considered an upper limit on the distance to PG 1553+113.