We present new Chandra X-ray observations of the transient black hole X-ray binary MAXI J1659-152 in quiescence. These observations were made more than one year after the end of the source's 2010-2011 outburst. We detect the source at a 0.5-10 keV flux of 2.8(8) × 10–15 erg s–1 cm–2, which corresponds to a luminosity of ~1.2 × 1031 (d/6 kpc)2 erg s–1. This level, while being the lowest at which the source has been detected, is within factors of ~2 of the levels seen at the end of the initial decay of the outburst and soon after a major reflare of the source. The quiescent luminosity of MAXI J1659-152, which is the shortest-orbital-period black hole X-ray binary (~2.4 hr), is lower than that of neutron-star X-ray binaries with similar periods. However, it is higher than the quiescent luminosities found for black hole X-ray binaries with orbital periods ~2-4 times longer. This could imply that a minimum quiescent luminosity may exist for black hole X-ray binaries, around orbital periods of ~5-10 hr, as predicted by binary-evolution models for the mass transfer rate. Compared to the hard state, we see a clear softening of the power-law spectrum in quiescence, from an index of 1.55(4) to an index of 2.5(4). We constrain the luminosity range in which this softening starts to (0.18-6.2) × 10–5 (d/6 kpc)2 (M/8 M ☉) L Edd, which is consistent with the ranges inferred for other sources.