Estimation of animal density is fundamental to ecology, and ecologists often pursue density estimates using grids of detectors (e.g., cameras, live traps, hair snags) to sample animals at a study site. However, under such a framework, reliable estimates can be difficult to obtain because animals move on and off of the site during the sampling session (i.e., the site is not closed geographically). Generally, practitioners address lack of geographic closure by inflating the area sampled by the detectors based on the mean distance individuals moved between trapping events or invoking hierarchical models in which animal density is assumed to be a spatial point process, and detection is modeled as a declining function of distance to a detector. We provide an alternative in which lack of geographic closure is sampled directly using telemetry, and this auxiliary information is used to compute estimates of density based on a modified Huggins closed-capture estimator. Contrary to other approaches, this method is free from assumptions regarding the distribution and movement of animals on the landscape, the stationarity of their home ranges, and biases induced by abnormal movements in response to baited detectors. The estimator is freely available in Program MARK.