Questions as to what drove the bulk reionization of the universe, how that reionization proceeded, and how the hard ionizing radiation reached the intergalactic medium remain open and debated. Observations probing that epoch are severely hampered by the increasing amounts of neutral gas with increasing redshift, so a small, but growing, number of experiments are targeting star-forming galaxies (z ~ 3) as proxies. However, these studies, while providing fantastic detail, are time intensive, contain relatively few targets, and can suffer from selection biases. As a complementary alternative, we investigate whether stacking the already vast (and growing) numbers of low-resolution (Δλ/λ = 800) Lyα-emitting (LAE) galaxy spectra from the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) can be used to measure ionizing photons (rest-frame 880-910 Å) escaping their galaxy hosts. As a blind survey, HETDEX avoids the biases from continuum-selected galaxies, and its planned 540 deg2 coverage promotes the statistical power of large numbers. In this paper, we confirm the feasibility of Lyman continuum detection by carefully selecting a sample of 214 high-redshift (z ~ 3) LAEs from a subset of HETDEX observations, stacking their spectra and measuring a ≳3σ detection of 0.10 μJy rest-frame Lyman continuum emission, uncorrected for attenuation in the intergalactic medium, over the full sample stack (3.0 < z < 3.5 and -22.0 ≲ MUV ≲ -19.0).