Interest in the superconducting proximity effect has recently been reignited by theoretical predictions that it could be used to achieve topological superconductivity. Low-Tc superconductors have predominantly been used in this effort, but small energy scales of ~1 meV have hindered the characterization of the emergent electronic phase, limiting it to extremely low temperatures. In this work, we use molecular beam epitaxy to grow topological insulator Bi2Te3 in a range of thicknesses on top of a high-Tc superconductor Fe(Te,Se). Using scanning tunneling microscopy and spectroscopy, we detect Δind as high as ~3.5 meV, which is the largest reported gap induced by proximity to an s-wave superconductor to-date. We find that Δind decays with Bi2Te3 thickness, but remains finite even after the topological surface states had been formed. Finally, by imaging the scattering and interference of surface state electrons, we provide a microscopic visualization of the fully gaped Bi2Te3 surface state due to Cooper pairing. Our results establish Fe-based high-Tc superconductors as a promising new platform for realizing high-Tc topological superconductivity.