Possible periodic activity in the repeating FRB 121102

The discovery that at least some Fast Radio Bursts (FRBs) repeat has ruled out cataclysmic events as the progenitors of these particular bursts. FRB~121102 is the most well-studied repeating FRB but despite extensive monitoring of the source, no underlying pattern in the repetition has previously been identified. Here, we present the results from a radio monitoring campaign of FRB~121102 using the 76-m Lovell telescope. Using the pulses detected in the Lovell data along with pulses from the literature, we report a detection of periodic behaviour of the source over the span of five years of data. We predict that the source is currently `off' and that it should turn `on' for the approximate MJD range $59002-59089$ (2020-06-02 to 2020-08-28). This result, along with the recent detection of periodicity from another repeating FRB, highlights the need for long-term monitoring of repeating FRBs at a high cadence. Using simulations, we show that one needs at least 100 hours of telescope time to follow-up repeating FRBs at a cadence of 0.5--3 days to detect periodicities in the range of 10--150 days. If the period is real, it shows that repeating FRBs can have a large range in their activity periods that might be difficult to reconcile with neutron star precession models.