  The photoproduction of eta-mesic 3He has been investigated using the TAPS
calorimeter at the Mainz Microtron accelerator facility MAMI. The total
inclusive cross section for the reaction gamma+3He->eta+X has been measured for
photon energies from threshold to 820 MeV. The total and angular differential
coherent eta cross sections have been extracted up to energies of 745 MeV. A
resonance-like structure just above the eta production threshold with an
isotropic angular distribution suggests the existence of a resonant quasi-bound
state. This is supported by studies of a competing decay channel of such a
quasi-bound eta-mesic nucleus into pi^0+p+X. A binding energy of (-4.4+-4.2)
MeV and a width of (25.6+-6.1) MeV is deduced for the quasi-bound eta-mesic
state in 3He.
