We present the results of a variability study of accreting young stellar objects in the Chameleon I star-forming region, based on ∼300 high-resolution optical spectra from the Fibre Large Area Multi-Element Spectrograph (FLAMES) at the European Southern Observatory (ESO) Very Large Telescope (VLT). 25 objects with spectral types from G2–M5.75 were observed 12 times over the course of 15 months. Using the emission lines Hα (6562.81 Å) and Ca ii (8662.1 Å) as accretion indicators, we found 10 accreting and 15 non-accreting objects. We derived accretion rates for all accretors in the sample using the Hα equivalent width, Hα 10 per cent width and Ca ii (8662.1 Å) equivalent width. We found that the Hα equivalent widths of accretors varied by ∼7–100 Å over the 15-month period. This corresponds to a mean amplitude of variations in the derived accretion rate of ∼0.37 dex. The amplitudes of variations in the derived accretion rate from Ca ii equivalent width were ∼0.83 dex and those from Hα 10 per cent width were ∼1.11 dex. Based on the large amplitudes of variations in accretion rate derived from the Hα 10 per cent width with respect to the other diagnostics, we do not consider it to be a reliable accretion rate estimator. Assuming the variations in Hα and Ca ii equivalent width accretion rates to be closer to the true value, these suggest that the spread that was found around the accretion rate to stellar-mass relation is not due to the variability of individual objects on time-scales of weeks to ∼1 year. From these variations, we can also infer that the accretion rates are stable within <0.37 dex over time-scales of less than 15 months. A major portion of the accretion variability was found to occur over periods shorter than the shortest time-scales in our observations, 8–25 days, which are comparable with the rotation periods of these young stellar objects. This could be an indication that what we are probing is spatial structure in the accretion flows and it also suggests that observations on time-scales of ∼a couple of weeks are sufficient to limit the total extent of accretion-rate variations in typical young stars. No episodic accretion was observed: all 10 accretors accreted continuously for the entire period of observations and, though they may have undetected low accretion rates, the non-accretors never showed any large changes in their emission that would imply a jump in accretion rate.