Recently developed low-power Chip-Scale Atomic Clocks (CSACs) hold promise for underwater acoustics applications because they enable time-coherent processing, critical for estimating the directionality of the sound field, when acoustic array elements cannot share a timing reference. Controlled, tank-based experiments with a small acoustic array (N = 4) featuring CSAC-equipped elements show that optimal disciplining is important for continued array coherence. Clock drift equivalent to a 10% wavelength error at 0.3, 1, and 10 kHz was reached at approximately 25, 10, and 3 days, respectively. Within application-specific limits, this technology brings enhanced capabilities to acoustic thermometry, geoacoustic, biological, and under-ice acoustic oceanography.