We report on the HST detection of the Lyman-continuum (LyC) radiation emitted by a galaxy at redshift z=3.794, dubbed Ion1 (Vanzella et al. 2012). The LyC from Ion1 is detected at rest-frame wavelength 820$\sim$890 \AA with HST WFC3/UVIS in the F410M band ($m_{410}=27.60\pm0.36$ magnitude (AB), peak SNR = 4.17 in a circular aperture with radius r = 0.12'') and at 700$\sim$830 \AA with the VLT/VIMOS in the U-band ($m_U = 27.84\pm0.19$ magnitude (AB), peak SNR = 6.7 with a r = 0.6'' aperture). A 20-hr VLT/VIMOS spectrum shows low- and high-ionization interstellar metal absorption lines, the P-Cygni profile of CIV and Ly$\alpha$ in absorption. The latter spectral feature differs from what observed in known LyC emitters, which show strong Ly$\alpha$ 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, presumably because of lower dust obscuration. The F410M image shows that the centroid of the LyC emission is offset from the centroid of the non-ionizing UV emission by 0.12''$\pm$0.03'', corresponding to 0.85$\pm$0.21 kpc (physical), 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 HI column-density "cavities" in the ISM, possibly carved by stellar winds and/or supernova. We also collect the VIMOS U-band images of a sample of 107 Lyman-break galaxies with spectroscopic redshifts at $3.40Comment: 24 pages, 13 figures, accepted for publication in ApJ