We present the first measurement of the spatial clustering of mid-infrared-selected obscured and unobscured quasars, using a sample in the redshift range 0.7 <z <1.8 selected from the 9 deg2 Bo??tes multiwavelength survey. Recently, the Spitzer Space Telescope and X-ray observations have revealed large populations of obscured quasars that have been inferred from models of the X-ray background and supermassive black hole evolution. To date, little is known about obscured quasar clustering, which allows us to measure the masses of their host dark matter halos and explore their role in the cosmic evolution of black holes and galaxies. In this study, we use a sample of 806 mid-infrared-selected quasars and a??250,000 galaxies to calculate the projected quasar-galaxy cross-correlation function wp (R). The observed clustering yields characteristic dark matter halo masses of log(M halo [h -1 M aS?]) = 12.7 +0.4-0.6 and 13.3+0.3-0.4 for unobscured quasars (QSO-1s) and obscured quasars (Obs-QSOs), respectively. The results for QSO-1s are in excellent agreement with previous measurements for optically selected quasars, while we conclude that the Obs-QSOs are at least as strongly clustered as the QSO-1s. We test for the effects of photometric redshift errors on the optically faint Obs-QSOs, and find that our method yields a robust lower limit on the clustering; photo-z errors may cause us to underestimate the clustering amplitude of the Obs-QSOs by at most a??20 . We compare our results to previous studies, and speculate on physical implications of stronger clustering for obscured quasars.