Encoding of spatial information in magnetic resonance imaging is conventionally accomplished by using magnetic field gradients. During gradient encoding, the position in k-space is determined by a time-integral of the gradient field, resulting in a limitation in imaging speed due to either gradient power or secondary effects such as peripheral nerve stimulation. Partial encoding of spatial information through the sensitivity patterns of an array of coils, known as parallel imaging, is widely used to accelerate the imaging, and is complementary to gradient encoding. This paper describes the one-dimensional limit of parallel imaging in which all spatial localization in one dimension is performed through encoding by the radiofrequency (RF) coil. Using a one-dimensional array of long and narrow parallel elements to localize the image information in one direction, an entire image is obtained from a single line of k-space, avoiding rapid or repeated manipulation of gradients. The technique, called single echo acquisition (SEA) imaging, is described, along with the need for a phase compensation gradient pulse to counteract the phase variation contained in the RF coil pattern which would otherwise cause signal cancellation in each imaging voxel. Image reconstruction and resolution enhancement methods compatible with the speed of the technique are discussed. MR movies at frame rates of 125 frames per second are demonstrated, illustrating the ability to monitor the evolution of transverse magnetization to steady state during an MR experiment as well as demonstrating the ability to image rapid motion. Because this technique, like all RF encoding approaches, relies on the inherent spatially varying pattern of the coil and is not a time-integral, it should enable new applications for MRI that were previously inaccessible due to speed constraints, and should be of interest as an approach to extending the limits of detection in MR imaging.