Using early data from the Infrared Array Camera (IRAC) on the Spitzer Space Telescope, taken for the Great Observatories Origins Deep Survey (GOODS), we identify and study objects that are well detected at 3.6 μm but are very faint (and in some cases, invisible) in the Hubble Ultra Deep Field (HUDF) ACS and NICMOS images and in very deep VLT Ks-band imaging. We select a sample of 17 objects with fν(3.6 μm)/fν(z850) > 20. The analysis of their spectral energy distributions (SEDs) from 0.4 to 8.0 μm shows that the majority of these objects cannot be satisfactorily explained without a well-evolved stellar population. We find that most of them can be well fitted by a simple two-component model, where the primary component represents a massive, old population that dominates the strong IR emission, while the secondary component represents a low-amplitude, on-going star formation process that accounts for the weak optical fluxes. Their estimated photometric redshifts (zp) range from 1.6 to 2.9 with the median at zp = 2.4. For the simple star formation histories considered here, their corresponding stellar masses range from (0.1-1.6)×1011 M☉ for a Chabrier initial mass function (IMF). Their median rest-frame Ks-band absolute magnitude is -22.9 mag in the AB system, or 1.5 × L*(K) for present-day elliptical galaxies. In the scenario of pure luminosity evolution, such objects may be direct progenitors for at least 14%-51% of the local population of early type galaxies. Because of the small cosmic volume of the HUDF, however, this simple estimate could be affected by other effects, such as cosmic variance and the strong clustering of massive galaxies. A full analysis of the entire GOODS area is now under way to assess such effects.