The rodent septohippocampal system contains "theta cells," which burst rhythmically at 4-12 Hz, but the functional significance of this rhythm remains poorly understood (Buzsáki, 2006). Theta rhythm commonly modulates the spike trains of spatially tuned neurons such as place (O'Keefe and Dostrovsky, 1971), head direction (Tsanov et al., 2011a), grid (Hafting et al., 2005), and border cells (Savelli et al., 2008; Solstad et al., 2008). An "oscillatory interference" theory has hypothesized that some of these spatially tuned neurons may derive their positional firing from phase interference among theta oscillations with frequencies that are modulated by the speed and direction of translational movements (Burgess et al., 2005, 2007). This theory is supported by studies reporting modulation of theta frequency by movement speed (Rivas et al., 1996; Geisler et al., 2007; Jeewajee et al., 2008a), but modulation of theta frequency by movement direction has never been observed. Here we recorded theta cells from hippocampus, medial septum, and anterior thalamus of freely behaving rats. Theta cell burst frequencies varied as the cosine of the rat's movement direction, and this directional tuning was influenced by landmark cues, in agreement with predictions of the oscillatory interference theory. Computer simulations and mathematical analysis demonstrated how a postsynaptic neuron can detect location-dependent synchrony among inputs from such theta cells, and thereby mimic the spatial tuning properties of place, grid, or border cells. These results suggest that theta cells may serve a high-level computational function by encoding a basis set of oscillatory signals that interfere with one another to synthesize spatial memory representations.