We present the first modeled search for gravitational waves using the complete binary black-hole gravitational waveform from inspiral through the merger and ringdown for binaries with negligible component spin. We searched approximately 2 years of LIGO data, taken between November 2005 and September 2007, for systems with component masses of 1-99Mȯ and total masses of 25-100Mȯ. We did not detect any plausible gravitational-wave signals but we do place upper limits on the merger rate of binary black holes as a function of the component masses in this range. We constrain the rate of mergers for 19Mȯ≤m1, m 2≤28Mȯ binary black-hole systems with negligible spin to be no more than 2.0Mpc-3Myr-1 at 90% confidence. © 2011 American Physical Society.