We have detected asymmetry in the symbiotic star CH Cyg through the measurement of precision closure phase with the Integrated Optics Near-Infrared Camera (IONIC) beam combiner, at the infrared optical telescope array interferometer. The position of the asymmetry changes with time and is correlated with the phase of the 2.1-year period found in the radial velocity measurements for this star. We can model the time-dependent asymmetry either as the orbit of a low-mass companion around the M giant or as an asymmetric, 20 per cent change in brightness across the M giant. We do not detect a change in the size of the star during a 3-year monitoring period neither with respect to time nor with respect to wavelength. We find a spherical dust shell with an emission size of 2.2 +/- 0.1 D* full width at half-maximum around the M giant star. The star to dust flux ratio is estimated to be 11.63 +/-0.3. While the most likely explanation for the 20 per cent change in brightness is non-radial pulsation, we argue that a low-mass companion in close orbit could be the physical cause of the pulsation. The combined effect of pulsation and low-mass companion could explain the behaviour revealed by the radial velocity curves and the time-dependent asymmetry detected in the closure-phase data. If CH Cyg is a typical long secondary period variable then these variations could be explained by the effect of an orbiting low-mass companion on the primary star.