This Letter reports the results from a haloscope search for dark matter axions with masses between 2.66 and 2.81 μeV. The search excludes the range of axion-photon couplings predicted by plausible models of the invisible axion. This unprecedented sensitivity is achieved by operating a large-volume haloscope at subkelvin temperatures, thereby reducing thermal noise as well as the excess noise from the ultralow-noise superconducting quantum interference device amplifier used for the signal power readout. Ongoing searches will provide nearly definitive tests of the invisible axion model over a wide range of axion masses.