  We demonstrate that the statistical behavior of random line shapes of single
tetra-tert-butylterrylene chromophores embedded in an amorphous polyisobutylene
matrix at T=2 K, is described by L\'evy statistics as predicted theoretically
by Barkai, Silbey, and Zumofen [{\em Phys. Rev. Lett.} {\bf 84} 5339 (2000)].
This behavior is a manifestation of the long range interaction between two
level systems in the glass and the single molecule. A universal amplitude ratio
is investigated which shows that the standard tunneling model assumptions are
compatible with the experimental data.
