  We compare [alpha/Fe], metallicity, and age distributions of globular
clusters in elliptical, lenticular, and spiral galaxies, which we derive from
Lick line index measurements. We find a large number of globular clusters in
elliptical galaxies that reach significantly higher [alpha/Fe] values (>0.5)
than any clusters in lenticular and spiral galaxies. Most of these extremely
alpha-enriched globular clusters are old (t > 8 Gyr) and cover the metallicity
range -1 <~ [Z/H] <~ 0. A comparison with supernova yield models suggests that
the progenitor gas clouds of these globular clusters must have been
predominantly enriched by massive stars (>~20 M_sol) with little contribution
from lower-mass stars. The measured [alpha/Fe] ratios are also consistent with
yields of very massive pair-instability supernovae (~130-190 M_sol). Both
scenarios imply that the chemical enrichment of the progenitor gas was
completed on extremely short timescales of the order of a few Myr. Given the
lower [alpha/Fe] average ratios of the diffuse stellar population in early-type
galaxies, our results suggest that these extremely alpha-enhanced globular
clusters could be members of the very first generation of star clusters formed,
and that their formation epochs would predate the formation of the majority of
stars in giant early-type galaxies.
