We report on the Hubble Space Telescope (HST) detection of the Lyman-continuum (LyC) radiation emitted by a galaxy at redshift z = 3.794 dubbed Ion1. The LyC from Ion1 is detected at 820−890 Å with HST WFC3/UVIS in the F410M band (m 410 = 27.60 ± 0.36 m AB, peak signal-to-noise ratio (S/N) = 4.17 in an r = 0farcs12 aperture) and 700−830 Å with the Very Large Telescope (VLT)/VIMOS in the U band (m U = 27.84 ± 0.19 m AB, peak S/N = 6.7 with an r = 0farcs6 aperture). A 20 hr VLT/VIMOS spectrum shows low- and high-ionization interstellar metal absorption lines and the P Cygni profile of C iv and Lyα in absorption. The latter spectral feature differs from what observed in known LyC emitters, which show strong Lyα emission. An HST far-UV color map reveals that the LyC emission escapes from a region of the galaxy that is bluer than the rest. The F410M image shows that the centroid of the LyC emission is offset from the centroid of the nonionizing UV emission by 0farcs12 ± 0farcs03, corresponding to 0.85 ± 0.21 kpc, and that its morphology is likely moderately resolved. These morphological characteristics favor a scenario where the LyC photons produced by massive stars escape from low H i column density "cavities" in the interstellar medium. We also collect the VIMOS U-band images of 107 Lyman-break galaxies at 3.40 < z spec < 3.95, i.e., sampling the LyC, and stack them with inverse-variance weights. No LyC emission is detected in the stacked image, resulting in a 32.5 m AB flux limit (1σ) and an upper limit of absolute LyC escape fraction f esc abs ≤ 0.63%.