A new Brillouin spectroscopic strategy has permitted us, for the first time, to obtain direct information about the values of the longitudinal elastic constant in the growth plane and in the growth direction (c(11) and c(33), respectively) of a Langmuir-Blodgett film of copper arachidate. The obtained results show the elastic isotropy of the film in the growth plane and the clear difference from the value obtained in directions almost parallel to the growth direction (c(11) = 9.4 +/- 0.1 GPa and c(33) > 10.59 GPa). This nondestructive and contactless method opens new perspectives in the determination of the elastic properties of thin film samples.