During an imaging survey of the Chamaeleon I star-forming region with the Advanced Camera for Surveys aboard the Hubble Space Telescope, we have discovered a candidate substellar companion to the young low-mass star CHXR 73 (τ ~ 2 Myr, M ~ 0.35 M). We measure a projected separation of 130 ± 003 for the companion, CHXR 73 B, which corresponds to 210 AU at the distance of the cluster. A near-infrared spectrum of this source obtained with the Cornell Massachusetts Slit Spectrograph at the Magellan II telescope exhibits strong steam absorption that confirms its late-type nature (M9.5). In addition, the gravity-sensitive shapes of the H- and K-band continua demonstrate that CHXR 73 B is a young, pre-main-sequence object, rather than a field star. The probability that CHXR 73 A and B are unrelated members of Chamaeleon I is ~0.001. We estimate the masses of CHXR 73 B and other known substellar companions in young clusters with a method that is consistent with the dynamical measurements of the eclipsing binary brown dwarf 2M 0535-0546, which consists of a comparison of the bolometric luminosities of the companions to the values predicted by the evolutionary models of Chabrier et al. and Burrows et al. We arrive at mass estimates of 0.003-0.004, 0.024 ± 0.012, 0.011, and 0.012 M for 2M 1207-3932 B, GQ Lup B, DH Tau B, and CHXR 73 B, respectively. Thus, DH Tau B and CHXR 73 B appear to be the least massive companions to stars outside the solar system that have been detected in direct images, and may have masses that are within the range observed for extrasolar planetary companions (M 0.015 M). However, because these two objects (as well as 2M 1207-3932 B) probably did not form within circumstellar disks around their primaries, we suggest that they should be viewed as brown dwarf companions rather than planets.