In this paper, we estimate binary compact object merger detection rates for LIGO, including the potentially significant contribution from binaries that are produced in elliptical galaxies near the epoch of peak star formation. Specifically, we convolve hundreds of model realizations of elliptical- and spiral-galaxy population syntheses with a model for elliptical- and spiral-galaxy star formation history as a function of redshift. Our results favor local merger rate densities of 4x10^-3^Mpc^-3^/Myr for binary black holes (BHs), 3x10^-2^Mpc^-3^/Myr for binary neutron stars (NSs), and 10^-2^Mpc^-3^/Myr for BH-NS binaries. Assuming a detection signal-to-noise ratio threshold of 8 for a single detector (in practice as part of a network, to reduce its noise), corresponding to radii Dbns of the effective volume inside of which a single LIGO detector could observe the inspiral of two 1.4M_{sun}_ NSs of 14Mpc and 197Mpc, for initial and advanced LIGO, we find event rates of any merger type of 2.9x10^-2^-0.46 and 25-400yr^-1^ (at 90% confidence level), respectively.