  We have carried out a sensitive high-resolution imaging survey of stars in
the young (6-8 Myr), nearby (97 pc) compact cluster around eta Chamaeleontis to
search for stellar and sub-stellar companions. Given its youth and proximity,
any sub-stellar companions are expected to be luminous, especially in the near
infrared, and thus easier to detect next to their parent stars. Here, we
present VLT/NACO adaptive optics imaging with companion detection limits for 17
eta Cha cluster members, and follow-up VLT/ISAAC near-infrared spectroscopy for
companion candidates. The widest binary detected is ~0.2", corresponding to the
projected separation 20 AU, despite our survey being sensitive down to
sub-stellar companions outside 0.3", and planetary mass objects outside 0.5".
This implies that the stellar companion probability outside 0.3" and the brown
dwarf companion probability outside 0.5" are less than 0.16 with 95%
confidence. We compare the wide binary frequency of eta Cha to that of the
similarly aged TW Hydrae association, and estimate the statistical likelihood
that the wide binary probability is equal in both groups to be < 2e-4. Even
though the eta Cha cluster is relatively dense, stellar encounters in its
present configuration cannot account for the relative deficit of wide binaries.
We thus conclude that the difference in wide binary probability in these two
groups provides strong evidence for multiplicity properties being dependent on
environment. In two appendices we derive the projected separation probability
distribution for binaries, used to constrain physical separations from observed
projected separations, and summarize statistical tools useful for multiplicity
studies.
