  We present extensive photometric and spectroscopic observations of the Type
Ia supernova (SN Ia) 2000cx in the S0 galaxy NGC 524, which reveal it to be
peculiar. Photometrically, SN 2000cx is different from all known SNe Ia, and
its light curves cannot be fit well by the fitting techniques currently
available. There is an apparent asymmetry in the $B$-band peak, in which the
premaximum brightening is relatively fast (similar to that of the normal SN
1994D), but the postmaximum decline is relatively slow (similar to that of the
overluminous SN 1991T). The color evolution of SN 2000cx is also peculiar: the
$(B - V)_0$ color has a unique plateau phase and the $(V - R)_0$ and $(V -
I)_0$ colors are very blue.
  Although the premaximum spectra of SN 2000cx are similar to those of SN
1991T-like objects (with weak Si II lines), its overall spectral evolution is
quite different. The Si II lines that emerged near maximum $B$-band brightness
stay strong in SN 2000cx until about three weeks past maximum. The change in
the excitation stages of iron-peak elements is slow. Both the iron-peak and the
intermediate-mass elements are found to be moving at very high expansion
velocities in the ejecta of SN 2000cx.
  We discuss theoretical models for SN 2000cx. SN 2000cx may be an overluminous
object like SN 1991T, but with a larger yield of $^{56}$Ni and a higher kinetic
energy in the ejecta. We also briefly discuss the implications of our
observations for the luminosity vs. light-curve width relation.
