Stellar-mass black holes (BHs) are mostly found in x-ray transients, a subclass of x-ray binaries that exhibit violent outbursts. None of the 50 galactic BHs known show eclipses, which is surprising for a random distribution of inclinations. Swift J1357.2-093313 is a very faint x-ray transient detected in 2011. On the basis of spectroscopic evidence, we show that it contains a BH in a 2.8-hour orbital period. Further, high-time-resolution optical light curves display profound dips without x-ray counterparts. The observed properties are best explained by the presence of an obscuring toroidal structure moving outward in the inner disk, seen at very high inclination. This observational feature should play a key role in models of inner accretion flows and jet collimation mechanisms in stellar-mass BHs.