We use data from the first epoch of observations with the IRAC/Spitzer for the GOODS to detect and study a collection of LBGs at z ~ 6 to 5 in the HUDF, six of which have spectroscopic confirmation. At these redshifts, IRAC samples rest-frame optical light in the range 0.5 to 0.8 um, where the effects of dust extinction are smaller and the sensitivity to light from evolved stars is greater than at shorter, rest-frame UV observable from the ground or with the HST. As such, it provides useful constraints on the ages and masses of these galaxies stellar populations. We find that the SEDs for many of these galaxies are best fitted by models of stellar populations with masses of a few x 1e10 M_sun, and with ages of a few hundred Myrs, values quite similar to those derived for typical LBGs at z ~ 3. When the universe was only 1 Gyr old, some galaxies had already formed a mass of stars approaching that of the present-day Milky Way, and that they started forming those stars at z > 7, and in some cases much earlier. We find that the lower limits to the space density for galaxies in this mass range are consistent with predictions from recent hydrodynamic simulations of structure formation in a LCDM universe. All objects in our samples are consistent with having solar metallicity, suggesting that they might have already been significantly polluted by metals. The values for dust reddening derived from the model fitting are low or zero, and we find that some of the galaxies have rest-frame UV colors that are even bluer than those predicted by the stellar population models to which we compare them. These colors might be attributed to the presence of very massive stars (> 100 M_sun), or by weaker intergalactic HI absorption than what is commonly assumed.