Context : The star-forming regions in Chamaeleon ( Cha ) are one of the nearest ( distance \sim 165 pc ) and youngest ( age \sim 2 Myrs ) conglomerates of recently formed stars and the ideal target for population studies of star formation . Aims : We investigate a total of 16 Cha targets , which have been suggested , but not confirmed as 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 arcseconds , 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 PMD´s , 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 _ { \sun } ) , 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 .