Testing Cold Dark Matter with the hierarchical buildup of stellar light

(Abridged) We demonstrate that the tenet of hierarchical structure growth leads directly to a robust, falsifiable prediction for the correlation between stellar fraction (fstar) and total system mass (M500) of galaxy groups and clusters. This prediction is relatively insensitive to the details of baryonic physics or cosmological parameters. In particular, if the fstar-M500 relation is fixed and does not evolve with redshift, CDM models predict the logarithmic slope of this relation to be b>-0.3. This constraint can be weakened if the fstar-M500 relation evolves strongly, but this implies more stars must be formed in situ in groups at low redshift. Conservatively requiring that at least half the stars in groups were formed by z=1, the constraint from evolution models is b>-0.35. Since the most massive clusters (M500=1E15 Msun) are observed to have fstar=0.01, this means that groups with M500=5E13 Msun must have fstar<0.03. Recent observations by Gonzalez et al. (2007) indicate a much steeper relation, with fstar>0.04 in groups, leading to b=-0.64. If confirmed, this would rule out hierarchical structure formation models: today's clusters could not have been built from today's groups, or even from the higher-redshift progenitors of those groups. We perform a careful analysis of these and other data to identify the most important systematic uncertainties in their measurements. Although correlated uncertainties on stellar and total masses might explain the steep observed relation, the data are only consistent with theory if the observed group masses are systematically underestimated.