We report the discovery of high-energy γ-ray emission from the Broad Line Radio Galaxy (BLRG) Pictor A with a significance of ~5.8σ (TS=33.4), based on three years of observations with the Fermi Large Area Telescope (LAT) detector. The three-year averaged E>0.2 GeV γ-ray spectrum is adequately described by a power-law, with a photon index, Γ, of $2.93 ± 0.03$ and a resultant integrated flux of $F_{γ}=(5.8±0.7) \times 10^{-9}$ ph cm$^{-2}$s$^{-1}$. A temporal investigation of the observed γ-ray flux, which binned the flux into year long intervals, reveals that the flux in the third year was 50% higher than the three-year average flux. This observation, coupled with the fact that this source was not detected in the first two years of {Fermi-LAT observations, suggests variability on timescales of a year or less. Synchrotron Self-Compton modelling of the spectral energy distribution of a prominent hot-spot in Pictor A's western radio lobe is performed. It is found that the models in which the γ-ray emission originates within the lobes, predicts an X-ray flux larger than that observed. Given that the X-ray emission in the radio lobe hot-spots has been resolved with the current suite of X-ray detectors, we suggest that the γ-ray emission from Pictor A originates from within its jet, which is in agreement with other γ-ray loud BLRGs. This suggestion is consistent with the evidence that the γ-ray flux is variable on timescales of a year or less. ; Comment: Accepted for publication in MNRAS: 8 pages, 3 figures, 1 table