In this paper, we propose a new type of array antenna, termed the Random Frequency Diverse Array (RFDA), for an uncoupled indication of target direction and range with low system complexity. In RFDA, each array element has a narrow bandwidth and a randomly assigned carrier frequency. The beampattern of the array is shown to be stochastic but thumbtack-like, and its stochastic characteristics, such as the mean, variance, and asymptotic distribution are derived analytically. Based on these two features, we propose two kinds of algorithms for signal processing. One is matched filtering, due to the beampattern's good characteristics. The other is compressive sensing, because the new approach can be regarded as a sparse and random sampling of target information in the spatial-frequency domain. Fundamental limits, such as the Cramér-Rao bound and the observing matrix's mutual coherence, are provided as performance guarantees of the new array structure. The features and performances of RFDA are verified with numerical results.