In order to derive information on the star formation history in the early universe, we observed six high-redshift (z ≃ 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 ≃ 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 Supernovae (SNe II), while iron is formed predominantly in SNe la with a delay of ∼1 Gyr and assuming as cosmological parameters H₀ = 72 km s^-1 Mpc^-1, ω_M = 0.3, and ω_λ = 0.7, we conclude that major star formation activity in the host galaxies of our z ≃ 3.4 quasars must have started already at an epoch corresponding to z_f ≃ 10, when the age of the universe was less than 0.5 Gyr.