This document presents the scientific justification and the conceptual design for the "Next Linear Collider Test Accelerator" (NLCTA) at SLAC. The goals of the NLCTA are to integrate the new technologies of X-band accelerator structures and rf systems being developed for the Next Linear Collider, to measure the growth of the "dark current" generated by rf field emission in the accelerator, to demonstrate multibunch beam-loading energy compensation and suppression of higher-order deflecting modes, and to measure any transverse components of the accelerating field.The NLCTA will be a 42-meter-long beam line consisting, consecutively, of a thermionic-cathode gun, an X-band buncher, a magnetic chicane, six 1.8-meter-long sections of 11.4-GHz accelerator structure, and a magnetic spectrometer. Initially, the unloaded accelerating gradient will be 50 MV/ m. A higher-gradient upgrade option eventually would increase the unloaded gradient to 100 MV/m. V * Elastance is defined as wR/Q per unit length.