ABSTRACT We present Lyman continuum (LyC) radiation escape fraction (fesc) measurements for 183 spectroscopically confirmed star-forming galaxies in the redshift range 3.11 < z < 3.53 in the Chandra Deep Field South. We use ground-based imaging to measure fesc, and use ground- and space-based photometry to derive galaxy physical properties using spectral energy distribution (SED) fitting. We additionally derive O iii  +  H β equivalent widths (that fall in the observed K band) by including nebular emission in SED fitting. After removing foreground contaminants, we report the discovery of 11 new candidate LyC leakers at ≳ 2σ level, with fesc in the range 0.14−0.85. From non-detections, we place 1σ upper limits of fesc <0.12, where the Lyman-break selected galaxies have fesc <0.11 and ‘blindly’ discovered galaxies with no prior photometric selection have fesc <0.13. We find a slightly higher 1σ limit of fesc <0.20 from extreme emission line galaxies with rest-frame O iii  +  H β equivalent widths >300 Å. For candidate LyC leakers, we find a weak negative correlation between fesc and galaxy stellar masses, no correlation between fesc and specific star-formation rates (sSFRs) and a positive correlation between fesc and EW0(O iii  +  H β). The weak/no correlations between stellar mass and sSFRs may be explained by misaligned viewing angles and/or non-coincident time-scales of starburst activity and periods of high fesc. Alternatively, escaping radiation may predominantly occur in highly localized star-forming regions, or fesc measurements may be impacted by stochasticity of the intervening neutral medium, obscuring any global trends with galaxy properties. These hypotheses have important consequences for models of reionization.