Recent years have seen a substantial improvement both in photometry of low-luminosity stars in globular clusters and in modeling the stellar atmospheres of late-type dwarfs. We build on these observational and theoretical advances in undertaking the first determination of the distance to a globular cluster by main-sequence fitting using stars on the lower main sequence. The calibrating stars are extreme M subdwarfs, as classified by Gizis, with parallaxes measured to a precision of better than 10%. Matching against King et al.'s deep [V, (V-I)] photometry of NGC 6397, and adopting E_B-V = 0.18 mag, we derive a true distance modulus of 12.13 ± 0.15 mag for the cluster. This compares with (m - M)₀ = 12.24 ± 0.1 derived through conventional main-sequence fitting in the [V, (B-V)] plane. Allowing for intrinsic differences due to chemical composition, we derive a relative distance modulus of δ(m - M)₀ = 2.58 mag between NGC 6397 and the fiducial metal-poor cluster M92. We extend this calibration to other metal-poor clusters and examine the resulting RR Lyrae (M_V, [Fe/H]) relation.