We present a method for the measurement of spatially variable signal-to-noise (S/N) ratios in multichannel teleseismic receiver function (RF) images. The S/N ratio is defined as a measure of coherency of the final image, and the approach is applicable to any RF imaging technique that employs mapping of the records into depth followed by their summation as the final signal enhancement step. In such methods, all of the converted phases become horizontally aligned in the depth domain, and their coherent (signal) and incoherent (noise) components can be estimated by using stacking statistics. For 10 locations along two subarrays of the Continental Dynamics of Rocky Mountains Project (CD-ROM) teleseismic array, after a limited RF editing, we apply our method to the image resulting from three-dimensional (3-D) prestack RF depth migration. The resulting amplitude S/N values to vary from 0.1 to 0.3 in the individual RFs and from 1 to 5 in the final image, with significant spatial variability. These moderate S/N values argue in favor of sampling redundancy achieved in array recording and multichannel RF processing. In order to further reduce noise in RF images, denser and longer deployments or additional signal enhancement techniques are advisable. Because of its ability to provide direct assessment of image quality in three dimensions, including its dependence on the frequency band and data coverage, our method can also be potentially used for real-time array tuning and image focusing required for moving arrays proposed for the USArray program.