We present deep BV I observations of the core of M35 and a nearby comparison field obtained at the WIYN 3.5m telescope under excellent seeing conditions. These observations probe to V > 26, and display the lower main sequence in BV and V I CMDs down to V = 23.3 and 24.6, respectively. At these faint magnitudes the background Galactic field stars are far more numerous than the cluster stars, yet by using a smoothing technique and CMD density distribution subtraction we are able to recover the cluster fiducial main sequence and luminosity function to V = 24.6. We find the location of the M35 main sequence in these CMDs to be consistent with earlier work on other open clusters, specifically NGC 188, NGC 2420, and NGC 2477. We compare these open cluster fiducial sequences to stellar models by Baraffe et al. (1998), Siess et al. (2000), Girardi et al. (2000), and Yi et al. (2001) and find that the models are too blue in both B − V and V − I for stars less massive than 0.4 M. At least part of the problem appears to be underestimated opacity in the bluer bandpasses, with the amount of missing opacity increasing toward the blue. M35 contains stars to the limit of the extracted main sequence, at M 0.10–0.15 M, suggesting that M35 may harbor a large number of brown dwarfs, which should be easy targets for sensitive near-IR instrumentation on 8–10m telescopes. We also identify a new candidate white dwarf in M35 at V = 21.36± 0.01. Depending on which WD models are used in interpreting this cluster candidate, it is either a very high mass WD (1.05 ± 0.05 M) somewhat older (0.19–0.26 Gyr, 3–4) than our best isochrone age (150 Myr), or it is a modestly massive WD (0.67–0.78 M) much too old (0.42–0.83 Gyr) to belong to the cluster. Follow-up spectroscopy is required to resolve this issue.