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We observe spontaneous Hawking radiation, stimulated by quantum vacuum fluctuations, emanating from an analogue black hole in an atomic Bose-Einstein condensate. The Hawking radiation is observed via the correlations between the Hawking radiation exiting the black hole and the partner particles falling into the black hole. The quantum nature of the Hawking radiation is observed through entanglement, by comparing the Fourier transform of the corre-lations to a measurement of the population. This comparison shows that the experiment is well within the quantum regime, since the measured Hawking temperature determined from the population distribution is far below the upper limit for quantum entanglement. A broad energy spectrum of entangled Hawking pairs are observed. Maximal entanglement is ob-served for the high energy part of the Hawking spectrum, while the lowest energies are not entangled. Thermal behavior is seen at very low energies where the finite extent of the corre-lation function implies frequency dependence. Thermal behavior is also seen at high energies through the agreement of the correlation spectrum with the appropriate function of the Planck distribution. Further insight is obtained by a preliminary experiment in which the horizon is caused to oscillate at a fixed frequency, which stimulates waves travelling into and out of the black hole. The rate of particle production by the oscillating horizon is consistent with the measured Hawking temperature. Furthermore, the observed ratio of the phase velocities of the Hawking and partner particles are consistent with this preliminary ex-periment, as is the width of the Hawking/partner correlation feature. Additional confirmation of the results is obtained through a numerical simulation, which demonstrates that the Hawk-ing radiation occurs in an approximately stationary background. It also confirms the width of the Hawking/partner correlation feature. The measurement reported here verifies Hawking’s calculation, which is viewed as a milestone in the quest for quantum gravity. The observation of Hawking radiation and its entanglement verifies important elements in the discussion of information loss in a real black hole.