The laser-induced fluorescence spectra of single tetracene (C18H12) and pentacene (C24H14) molecules embedded in liquid He-N droplets ((N) over tilde similar or equal to 10(4)) show sharp zero phonon lines (ZPL) (delta nu less than or equal to 0.2 cm(-1)), accompanied by weaker phonon wings (PW) on the blue side. The ZPL of tetracene is anomalously split into a doublet with a separation of 1.1 cm(-1), whereas for pentacene, the ZPL is not split. Hole-burning measurements with two pulsed dye lasers and lifetime measurements indicate that inside He droplets the ground and excited states of tetracene are each split into two levels. The splitting is attributed either to the; occupation of two nearly equivalent sites by localized helium atoms or to a tunneling of one or two localized helium atoms through the barrier in the double-well potential on the surface of the tetracene molecule.