We present an upper limit for the relative escape fraction ( f _ { esc } ^ { rel } ) of ionizing radiation at z \sim 3.3 using a sample of 11 Lyman Break Galaxies ( LBGs ) with deep imaging in the U band obtained with the Large Binocular Camera , mounted on the prime focus of the Large Binocular Telescope . We selected 11 LBGs with secure redshift in the range 3.27 < z < 3.35 , from 3 independent fields . We stacked the images of our sources in the R and U band , which correspond to an effective rest-frame wavelength of 1500Å and 900Å respectively , obtaining a limit in the U band image of \geq 30.7 ( AB ) mag at 1 \sigma . We derive a 1 \sigma upper limit of f _ { esc } ^ { rel } \sim 5 \% , which is one of the lowest values found in the literature so far at z \sim 3.3 . Assuming that the upper limit for the escape fraction that we derived from our sample holds for all galaxies at this redshift , the hydrogen ionization rate that we obtain ( \Gamma _ { -12 } < 0.3 s ^ { -1 } ) is not enough to keep the IGM ionized and a substantial contribution to the UV background by faint AGNs is required . Since our sample is clearly still limited in size , larger z \sim 3 LBG samples , at similar or even greater depths are necessary to confirm these results on a more firm statistical basis .