  The experimental setup and results of the first search for invisible decays
of ortho-positronium (o-Ps) confined in a vacuum cavity are reported. No
evidence of invisible decays at a level
$\text{Br}\left(\text{o-Ps}\to\text{invisible}\right) < 5.9\times 10^{-4}$ (90%
C. L.) was found. This decay channel is predicted in Hidden Sector models such
as the Mirror Matter (MM), which could be a candidate for Dark Matter. Analyzed
within the MM context, this result provides an upper limit on the kinetic
mixing strength between ordinary and mirror photons of $\epsilon < 3.1 \times
10^{-7}$ (90% C. L.). This limit was obtained for the first time in vacuum free
of systematic effects due to collisions with matter.
