We present results of high-cadence monitoring of the optical light curve of the nearby, Type Ia SN 2014J in M82, using the 2.3m Aristarchos telescope. B and V-band photometry on days 15-18 after tmax(B) was obtained with a cadence of 2 min per band, revealing evidence for rapid variability at the 0.02-0.05mag level on timescales of 15-60min on all four nights. The decline slope was measured as steeper in the B-band than in the V-band, and to steadily decrease in both bands from 0.15 mag/day (night 1) to 0.04mag/day (night 4) in V, and from 0.19mag/day (night 1) to 0.06mag/day (night 4) in B, corresponding to the onset of the secondary maximum. We propose that rapid variability could be due to one or a combination of the following scenarios: the clumpiness of the ejecta, their interaction with circumstellar material, the asymmetry of the explosion, or the mechanism causing the secondary maximum in the near-infrared light curve. We encourage the community to undertake high-cadence monitoring of future, nearby and bright supernovae to investigate the intraday behaviour of their light curves.