We examine the role of environment on the in situ star formation (SF) hosted by the progenitors of the most massive galaxies in the present-day universe, the brightest cluster galaxies (BCGs), from $z sim 3$ to present in the COSMOS field. Progenitors are selected from the COSMOS field using a stellar mass cut motivated by the evolving cumulative comoving number density of progenitors within the Illustris simulation, as well as the Millennium-II simulation and a constant comoving number density method for comparison. We characterize each progenitor using far-ultraviolet--far-infrared observations taken from the COSMOS field and fitting stellar, dust, and active galactic nucleus components to their spectral energy distributions. Additionally, we compare the SF rates of our progenitor sample to the local density maps of the COSMOS field to identify the effects of environment. We find that BCG progenitors evolve in three stages, starting with an in situ SF dominated phase ($z > 2.25$). This is followed by a phase until $z sim 1.25$ where mass growth is driven by in situ SF and stellar mass deposited by mergers (both gas rich and poor) on the same order of magnitude independent of local environment. Finally, at low redshift dry mergers are the dominant stellar mass generation process. We also identify this final transition period as the time when progenitors quench, exhibiting quiescent NUVemph{rJ} colors.
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