In order to derive information on the star formation history in the early universe we observed 6 high-redshift ( z \simeq 3.4 ) quasars in the near-infrared to measure the relative iron and Mg ii emission strengths . A detailed comparison of the resulting spectra with those of low-redshift quasars show essentially the same Fe ii /Mg ii emission ratios and very similar continuum and line spectral properties , indicating a lack of evolution of the relative iron to magnesium abundance of the gas since z \simeq 3.4 in bright quasars . On the basis of current chemical evolution scenarios of galaxies , where magnesium is produced in massive stars ending in type II SNe , while iron is formed predominantly in SNe of type Ia with a delay of \sim 1 Gyr and assuming as cosmological parameters H _ { o } = 72 km s ^ { -1 } Mpc ^ { -1 } , \Omega _ { M } = 0.3 , and \Omega _ { \Lambda } = 0.7 , we conclude that major star formation activity in the host galaxies of our z \simeq 3.4 quasars must have started already at an epoch corresponding to z _ { f } \simeq 10 , when the age of the universe was less than 0.5 Gyrs .