Stars of late-M and L spectral types, collectively known as ultracool dwarfs (UCDs), may be excellent targets for searches for extrasolar planets. Owing to their small radii, the signal from an Earth-size planet transiting a UCD is, in principle, readily detectable. We present results from a study designed to evaluate the feasibility of using precise near-infrared (NIR) photometry to detect terrestrial extrasolar planets orbiting UCDs. We used the Peters Automated Infrared Imaging Telescope (PAIRITEL) to observe a sample of 13 UCDs over a period of 10 months. We consider several important systematic effects in NIR differential photometry and develop techniques for generating photometry with a precision of 0.01 mag and long-term stability. We simulate the planet detection efficiency of an extended campaign to monitor a large sample of UCDs with PAIRITEL. We find that both a targeted campaign with a single telescope lasting several years and a campaign making use of a network of telescopes distributed in longitude could provide significant sensitivity to terrestrial planets orbiting UCDs, potentially in the habitable zone.