The molecular mechanisms that drive circadian (24 h) rhythmicity have been investigated for many decades, but we still do not have a complete picture of eukaryotic circadian systems. Although the transcription/translation feedback loop (TTFL) model has been the primary focus of research, there are many examples of circadian rhythms that persist when TTFLs are not functioning, and we lack any good candidates for the non-TTFL oscillators driving these rhythms. In this hypothesis-driven review, the author brings together several lines of evidence pointing towards the Target of Rapamycin (TOR) signalling pathway as a good candidate for a non-TTFL oscillator. TOR is a ubiquitous regulator of metabolism in eukaryotes and recent focus in circadian research on connections between metabolism and rhythms makes TOR an attractive candidate oscillator. In this paper, the evidence for a role for TOR in regulating rhythmicity is reviewed, and the advantages of TOR as a potential oscillator are discussed. Evidence for extensive feedback regulation of TOR provides potential mechanisms for a TOR-driven oscillator. Comparison with ultradian yeast metabolic cycles provides an example of a potential TOR-driven self-sustained oscillation. Unanswered questions and problems to be addressed by future research are discussed.