Context. Determining the strength of the Lyman continuum (LyC) and the fraction of LyC escape have implications for the properties of the emitting sources at any redshift, but also for the re-ionization of the Universe at z > 6. Aims. We aim to measure the LyC signal from a sample of sources in the Chandra deep field south. We collect star-forming galaxies (SFGs) and active galactic nuclei (AGN) with accurate spectroscopic redshifts, for which Hubble Space Telescope (HST) coverage and multi-wavelength photometry are available. Methods. We selected a sample of about 200 sources at z ~ 3. Taking advantage of HST resolution, we applied a careful cleaning procedure and rejected sources showing nearby clumps with different colours, which could be lower-z interlopers. Our clean sample consisted of 86 SFGs (including 19 narrow-band selected Lyα emitters) and 8 AGN (including 6 detected in X-rays). We measured the LyC flux from aperture photometry in four narrow-band filters covering wavelengths below a 912 Å rest frame (3.11 < z < 3.53). We estimated the ratio between ionizing (LyC flux) and 1400 Å non-ionizing emissions for AGN and galaxies. Results. By running population synthesis models, we assume an average intrinsic Lν(1400 Å)/Lν(900 Å) ratio of 5 as the representative value for our sample. With this value and an average treatment of the lines of sight of the inter-galactic medium, we estimate the LyC escape fraction relative to the intrinsic value (fescrel(LyC)). We do not directly detect ionizing radiation from any individual SFG, but we are able to set a 1(2)σ upper limit of fescrel(LyC) < 12(24)%. This result is consistent with other non-detections published in the literature. No meaningful limits can be calculated for the sub-sample of Lyα emitters. We obtain one significant direct detection for an AGN at z = 3.46, with fescrel(LyC) = (72 ± 18)%. Conclusions. Our upper limit on fescrel(LyC) implies that the SFGs studied here do not present either the physical properties or the geometric conditions suitable for efficient LyC-photon escape.