Context. The star-forming regions in Chamaeleon (Cha) are one of the nearest (distance ∼ 165 pc) and youngest (age ∼ 2 Myr) conglomerates of recently formed stars and the ideal target for population studies of star formation. Aims. We investigate a total of 16 Cha targets that have been suggested, but not confirmed, to be binaries or multiple systems in previous literature. Methods. We used the adaptive optics instrument Naos-Conica (NACO) at the Very Large Telescope Unit Telescope (UT) 4 / YEPUN of the Paranal Observatory, at 2-5 different epochs, in order to obtain relative and absolute astrometric measurements, as well as differential photometry in the J, H, and K band. On the basis of known proper motions and these observations, we analyse the astrometric results in our proper motion diagram (PMD: angular separation / position angle versus time), to eliminate possible (non-moving) background stars, establish co-moving binaries and multiples, and search for curvature as indications for orbital motion. Results. All previously suggested close components are co-moving and no background stars are found. The angular separations range between 0.07 and 9 arcsec, corresponding to projected distances between the components of 6-845 AU. Thirteen stars are at least binaries and the remaining three (RX J0919.4-7738, RX J0952.7-7933, VW Cha) are confirmed high-order multiple systems with up to four components. In 13 cases, we found significant slopes in the PMDs, which are compatible with orbital motion whose periods (estimated from the observed gradients in the position angles) range from 60 to 550 years. However, in only four cases there are indications of a curved orbit, the ultimate proof of a gravitational bond. Conclusions. A statistical study based on the 2MASS catalogue confirms the high probability of all 16 stellar systems being gravitationally bound. Most of the secondary components are well above the mass limit of hydrogen burning stars (0.08 M ), and have masses twice as high as this value or more. Massive primary components appear to avoid the simultaneous formation of equal-mass secondary components, while extremely low-mass secondary components are hard to find for both high and low mass primaries owing to the much higher dynamic range and the faintness of the secondaries.