  We have performed narrow-band imaging observations with the Very Large
Telescope, aimed at detecting the Lyman continuum (LC) flux escaping from
galaxies at z~3. We do not find any significant LC flux from our sample of two
galaxies in the Hubble Deep Field South, at z=3.170 and 3.275. The
corresponding lower limits on the F_{1400}/F_{900} flux density (per Hz) ratio
are 15.6 and 10.2 (3-sigma confidence level). After correction for the
intergalactic hydrogen absorption, the resulting limits on the relative escape
fraction of the LC are compared with those obtained by different approaches, at
similar or lower redshifts. One of our two objects has a relative escape
fraction lower than the detection reported by Steidel et al. in a composite
spectrum of z~3 galaxies. A larger number of objects is required to reach a
significant conclusion. Our comparison shows the potential of narrow-band
imaging for obtaining the best limit on the relative escape fraction at z~3.
Stacking a significant number of galaxies observed through a narrow-band filter
would provide constraint on the galactic contribution to the cosmic
reionization.
