We present an unbiased catalog of calcium abundances for 517 red giants brighter that M(V) similar to -1 in the chemically inhomogeneous globular cluster omega Centauri. The basic features of the abundance distribution are as follows: (1) few, if any, stars exist on the giant branch of omega Cen with [Ca/H] less than -1.6; (2) there is a well-defined peak in the distribution at [Ca/H] = -1.4, with a long tail stretching up to similar to[Ca/H] similar to -0.3; and (3) the distribution is bimodal with a second smaller peak in the distribution at [Ca/H] = -0.9. The distribution may be well fitted by two components each having a simple closed box abundance distribution and for which the ratio of more metal rich to more metal poor is similar to 0.2. We argue that the present data, taken together with the abundance patterns of the s-process elements in this cluster reported by in 1994 by Vanture, Wallerstein, & Brown and in 1995 by Norris & Da Costa, are most convincingly described in terms of the two components representing successive epochs of star formation in the cluster, rather than of their being two independent merging fragments. Examination of the radial distribution of [Ca/H] suggests that there is an abundance gradient in the cluster, consistent with its having been formed in a dissipative manner. The picture emerges of omega Cen having evolved within the Searle-Zinn paradigm of Galactic globular cluster formation, from a gaseous protocloud of mass perhaps as large as similar to 10(8) M(.) and initial abundance [Ca/H] similar to -1.5 on a timescale similar to 1 Gyr, well away from the central region of the forming Galaxy and later coming into dynamical equilibrium with it.