Transient astronomical sources are typically powered by compact objects and usually signify highly explosive or dynamic events. While radio astronomy has an impressive record of obtaining high time resolution observations, usually it is achieved in quite narrow fields-of-view. Consequently, the dynamic radio sky is poorly sampled, in contrast to the situation in the X- and gamma -ray bands in which wide-field instruments routinely detect transient sources. Here we report a new transient source, GCRT J1745-3009, detected in 2002 during a moderately wide-field radio transient monitoring program of the Galactic center (GC) region at 0.33 GHz. The characteristics of its bursts are unlike those known for any other class of radio transient. If located in or near the GC, its brightness temperature ( 1016 K) and the implied energy density within GCRT J1745-3009 vastly exceeds that observed in most other classes of radio astronomical sources, and is consistent with coherent emission processes rarely observed. We conclude that GCRT J1745-3009 is the first member of a new class of radio transient sources, the first of possibly many new classes to be identified through current and upcoming radio surveys.