  We obtain positronium Hyperfine Splitting owing to the non-commutativity of
space and show that, in the leading order, it is proportional to $\theta
\alpha^6$ where, $\theta$ is the parameter of non-commutativity. It is also
shown that spatial non-commutativity splits the spacing between $n=2$ triplet
excited levels $E(2^3S_1)\to E(2^3P_2)$ which provides an experimental test on
the non-commutativity of space.
