First results on the scalar polarizability alpha 0 of a number of very highly excited p states of Cs (40 < or = n < or = 60), produced by one-step photoexcitation with frequency-doubled dye-laser radiation, were obtained by means of electrostatic beam deflection in a two-wire type electric field. Enormous polarizabilities of alpha 0/4 pi > 109 Å3 were measured; the dependence of the polarizability as a function of the principal quantum number n was found to be in agreement with the expected n7 behaviour.