In order to study the origin of the strong Ly \alpha emission of high-redshift starburst galaxies we observed and modeled the emission of the z = 3.304 galaxy FDF-4691 ( rest-frame EW _ { Ly \alpha } = 103 Å ) . The observations show that FDF-4691 is a young starburst galaxy with a ( for this redshift ) typical metallicity . The broad , double-peaked profile of the Ly \alpha emission line can be explained assuming a highly turbulent emission region in the inner part of the starburst galaxy , and a surrounding extended shell of low-density neutral gas with a normal dust/gas ratio and with Galactic dust properties . The detection of the Ly \alpha emission line is explained by the intrinsic broad Ly \alpha emission and a low HI column density of the neutral shell . A low dust/gas ratio in the neutral shell is not needed to explain the strong Ly \alpha line .