  We present the results of a multiplicity survey of 126 stars spanning ~0.1-3
solar masses in the ~2-Myr-old Chamaeleon I star-forming region, based on
adaptive optics imaging with the ESO Very Large Telescope. Our observations
have revealed 30 binaries and 6 triples, of which 19 and 4, respectively, are
new discoveries. The overall multiplicity fraction we find for Cha I (~30%) is
similar to those reported for other dispersed young associations, but
significantly higher than seen in denser clusters and the field, for comparable
samples. Both the frequency and the maximum separation of Cha I binaries
decline with decreasing mass, while the mass ratios approach unity; conversely,
tighter pairs are more likely to be equal mass. We confirm that brown dwarf
companions to stars are rare, even at young ages at wide separations. Based on
follow-up spectroscopy of two low-mass substellar companion candidates, we
conclude that both are likely background stars. The overall multiplicity
fraction in Cha I is in rough agreement with numerical simulations of cloud
collapse and fragmentation, but its observed mass dependence is less steep than
predicted. The paucity of higher-order multiples, in particular, provides a
stringent constraint on the simulations, and seems to indicate a low level of
turbulence in the prestellar cores in Cha I.
