The fluorescence excitation spectra of single chromophores in a solid often consist of several components at low temperature, which is due to the interaction with matrix two-level systems (TLSs). For a number of terrylene molecules in n-hexadecane we observed electric-field-induced changes of the intensity and splitting of the spectral components. With some basic assumptions the data allow us to calculate all the characteristic parameters of a single TLS, viz., the (zero field) asymmetry, the tunnel parameter, and the permanent electric dipole moment. In one case we found an exceptionally large dipole moment of about 8 Debye. (C) 2003 American Institute of Physics.