The XENON100 experiment, in operation at the Laboratori Nazionali del Gran Sasso in Italy, is designed to search for dark matter weakly interacting massive particles (WIMPs) scattering off 62 kg of liquid xenon in an ultralow background dual-phase time projection chamber. In this Letter, we present first dark matter results from the analysis of 11.17 live days of nonblind data, acquired in October and November 2009. In the selected fiducial target of 40 kg, and within the predefined signal region, we observe no events and hence exclude spin-independent WIMP-nucleon elastic scattering cross sections above 3.4 × 10⁻⁴⁴ cm² for 55 GeV/c² WIMPs at 90% confidence level. Below 20 GeV/c², this result constrains the interpretation of the CoGeNT and DAMA signals as being due to spin-independent, elastic, light mass WIMP interactions.