  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.
