The diffuse extragalactic gamma-ray background in the MeV region is believe
d to be due to photons from radioactivity produced in supernovae throughout
the history of galaxies in the universe. In particular, gamma-ray line emi
ssion from the decay chain Ni-56 --> Co-56 --> Fe-56 provides the dominant
photon source (Clayton & Silk). Although iron synthesis occurs in all types
of supernovae, the contribution to the background is dominated by Type Ia
events due to their higher photon escape probabilities. Estimates of the st
ar formation history in the universe suggest a rapid increase by a factor s
imilar to 10 from the present to a redshift z(p) similar to 1.5, beyond whi
ch it either remains constant or decreases slowly. Little is known about th
e cosmological star formation history for redshift exceeding z similar to 5
. We integrate the observed star formation history to determine the cosmic
gamma-ray background (CGB) from the corresponding supernova rate history. I
n addition to gamma-rays from short-lived radioactivity in Type Ia supernov
ae (SN Ia's) and Type II, Ib, and Ic supernovae (SN II's, SN Ib's, SN Ic's)
we also calculate the minor contributions from long-lived radioactivities
(Al-26, Ti-44, Co-60, and electron-positron pair annihilation). The time-in
tegrated gamma-ray spectrum of model W10HMM (Pinto & Woosley) was used as a
template for Type II supernovae, and for SN Ia's we employ model W7 (Nomot
o et al.). Although progenitor evolution for Type Ia supernovae is not yet
fully understood, various arguments suggest delays of order 1-2 Gyr between
star formation and the production of SN Ia's. The effect of this delay on
the CCB is discussed. We emphasize the value of gamma-ray observations of t
he CGB in the MeV range as an independent tool for studies of the cosmic st
ar formation history. If the delay between star formation and SN Ia activit
y exceeds 1 Gyr substantially and/or the peak of the cosmic star formation
rate occurs at a redshift much larger than unity, the gamma-ray production
of SN Ia's would be insufficient to explain the observed CGB and a so far u
ndiscovered source population would be implied. Alternatively, the cosmic s
tar formation rate would have to be higher (by a factor 2-3) than commonly
assumed, which is in accord with several upward revisions reported in the r
ecent literature.