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The Parallel Ionizing Emissivity (PIE) Survey will measure the average escape fraction of ionizing radiation (f_esc) at 3.1<z<3.5 using a sample of virgul700 galaxies. Using 3-band imaging (F336W comma F625W comma and F814W) comma PIE will color-select U-dropout galaxies comma where LyC is sampled by the F336W band. Pure parallel orbits will enable us to observe a total area of virgul500 arcminelev2 divided over virgul75 truly independent fields distributed across the extragalactic sky. This sampling will minimize the effect of IGM absorption (correlated on scales of 10s of Mpc) on the measurement of f_esc. Likewise comma our proposed high spatial resolution HST imaging will avoid contamination by low-redshift galaxies. In addition to the HST imaging comma we are requesting 10 nights of coordinated observations with NOIRLab Gemini telescopes (in addition to guaranteed institutional access to 8-m class telescopes) to measure the spectroscopic redshifts of the LyC emitting candidates that we will identify. The proposed data comma combined with the spectroscopic followup of the selected Lyman break galaxies comma will allow us to measure escape fractions of 10% at 3-sigma by stacking virgul150 targets as faint as 0.4L*. We will calibrate the evolution of f_esc indicators out to zvirgul3.5--measuring f_esc as a function of star formation surface density comma Ly-alpha properties comma UV luminosity comma and UV colors. The proposed dataset will be a resource for the astronomical community for the foreseeable future comma more than doubling the existing area with deep HST U-band coverage comma and greatly increasing the number of sight-lines.