Recent observations have revealed that some Type Ia supernovae exhibit narrow, time-variable Na I D absorption features. The origin of the absorbing material is controversial, but it may suggest the presence of circumstellar gas in the progenitor system prior to the explosion, with significant implications for the nature of the supernova progenitors. We present the third detection of such variable absorption, based on six epochs of high-resolution spectroscopy of the Type Ia supernova SN 2007le from Keck and the HET. The data span ~3 months, from 5 days before maximum light to 90 days after maximum. We find that one component of the Na D absorption lines strengthened significantly with time, indicating a total column density increase of ~2.5 x 10^12 cm^-2. The changes are most prominent after maximum light rather than at earlier times when the UV flux from the SN peaks. As with SN 2006X, we detect no change in the Ca II H&K lines over the same time period, rendering line-of-sight effects improbable and suggesting a circumstellar origin for the absorbing material. Unlike the previous two SNe exhibiting variable absorption, SN 2007le is not highly reddened (E_B-V = 0.27 mag), also pointing toward circumstellar rather than interstellar absorption. Photoionization models show that the data are consistent with a dense (10^7 cm^-3) cloud or clouds of gas located ~0.1 pc from the explosion. These results broadly support the single-degenerate scenario previously proposed to explain the variable absorption, with mass loss from a nondegenerate companion star responsible for providing the circumstellar gas. We also present tentative evidence for narrow Halpha emission associated with the SN, which will require followup observations at late times to confirm. [abridged]