We present Lyman continuum (LyC) radiation escape fraction ( f esc ) 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 f esc , 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 disco v ery of 11 new candidate LyC leakers at (cid:3) 2 σ level, with f esc in the range 0.14 − 0.85. From non-detections, we place 1 σ upper limits of f esc < 0.12, where the Lyman-break selected galaxies have f esc < 0.11 and ‘blindly’ disco v ered galaxies with no prior photometric selection have f esc < 0.13. We find a slightly higher 1 σ limit of f esc < 0.20 from extreme emission line galaxies with rest-frame [O III ] + H β equi v alent widths > 300 Å. For candidate LyC leakers, we find a weak ne gativ e correlation between f esc and galaxy stellar masses, no correlation between f esc and specific star-formation rates (sSFRs) and a positive correlation between f esc and EW 0 ([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 f esc . Alternatively, escaping radiation may predominantly occur in highly localized star-forming regions, or f esc 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.