In September 2012, the free-falling, deep-diving instrument platform Deep Sound III descended to the bottom of the Tonga Trench, where it resided at a depth of 8515 m for almost 3 h, recording ambient noise data on four hydrophones arranged in a vertical L-shaped configuration. The time series from each of the hydrophones yielded the power spectrum of the noise over the frequency band 3 Hz to 30 kHz. The spatial coherence functions, along with the corresponding cross-correlation functions, were recovered from all available hydrophone pairs in the vertical and the horizontal. The vertical coherence and cross-correlation data closely follow the predictions of a simple theory of sea-surface noise in a semi-infinite ocean, suggesting that the seabed in the Tonga Trench is a very poor acoustic reflector, which is consistent with the fact that the sediment at the bottom of the trench consists of very-fine-grained material having an acoustic impedance similar to that of seawater. The horizontal coherence and cross-correlation data are a little more complicated, showing evidence of (a) bathymetric shadowing of the noise by the walls of the trench and (b) highly directional acoustic arrivals from the research vessel supporting the experiment.