Recently a Type Ic supernova, SN 1998bw, was discovered coincident with a g
amma-ray burst, GRB 980425. The supernova had unusual radio, optical, and s
pectroscopic properties. Among other things, it was especially bright for a
Type Ic both optically and in the radio, and it rose quickly to maximum. W
e explore here models based upon helium stars in the range 9-14 M-. and car
bon-oxygen stars 6-11 M-., which experience unusually energetic explosions
(kinetic energy 0.5-2.8 x 10(52) ergs). Bolometric light curves and multiba
nd photometry are calculated and compared favorably with observations. No s
pectroscopic data are available at this time, but both LTE and non-LTE spec
tra are calculated for the model that agrees best with the light curve, a c
arbon-oxygen core of 6 M-. exploded with a kinetic energy of 2.2 x 10(52) e
rgs. We also examine potential mechanisms for producing the observed gamma-
ray burst (GRB)-shock breakout and relativistic shock deceleration in circu
mstellar material. For spherically symmetric models, both fail to produce a
GRB of even the low luminosity inferred for GRB 980425. However, the high
explosion energies required to understand the supernova are in contrast to
what is expected for such massive stars and indicate that a new sort of exp
losion may have been identified, possibly the consequence of a collapsar. I
ndeed a more likely explanation for what was seen is a highly asymmetric ex
plosion in which the GRB was produced by mildly relativistic matter (Gamma
approximate to 5) running into circumstellar matter along the line of sight
to the Earth. The explosion itself was powered by black hole accretion and
jets, but unlike "ordinary" gamma-ray bursts, the jets were not of suffici
ent energy and duration to effectively reach large values of Gamma. They ma
y also not have been oriented in our direction. The ejected mass (but not t
he Ni-56 mass) and explosion energy are then smaller. Other associations be
tween luminous Type Ic supernovae and GRBs may exist and should be sought,
but most Type Ib and Type Ic supernovae do not make GRBs.