Microwave atomic clocks have traditionally served as the 'gold standard' for precision measurements of time and frequency. However, over the past decade, optical atomic clocks(1-6) have surpassed the precision of their microwave counterparts by two orders of magnitude or more. Extant optical clocks occupy volumes of more than one cubic metre, and it is a substantial challenge to enable these clocks to operate in field environments, which requires the ruggedization and miniaturization of the atomic reference and clock laser along with their supporting lasers and electronics(4,7,8,9). In terms of the clock laser, prior laboratory demonstrations of optical clocks have relied on the exceptional performance gained through stabilization using bulk cavities, which unfortunately necessitates the use of vacuum and also renders the laser susceptible to vibration-induced noise. Here, using a stimulated Brillouin scattering laser subsystem that has a reduced cavity volume and operates without vacuum, we demonstrate a promising component of a portable optical atomic clock architecture. We interrogate a Sr-88(+) ion with our stimulated Brillouin scattering laser and achieve a clock exhibiting short-term stability of 3.9 x 10(-14) over one second-an improvement of an order of magnitude over state-of-the-art microwave clocks. This performance increase within a potentially portable system presents a compelling avenue for substantially improving existing technology, such as the global positioning system, and also for enabling the exploration of topics such as geodetic measurements of the Earth, searches for dark matter and investigations into possible long-term variations of fundamental physics constants(10-12).