The molecular beam electric resonance technique has been used to examine the hyperfine spectrum of CsF to determine the nuclear quadrupole interaction of the cesium nucleus. A total of 95 transitions in vibrational states v=0-5 and rotational states J=1-8 have been included in a fit to determine the cesium nuclear quadrupole and spin-rotation interactions, the fluorine spin-rotation interaction, and the tensor and scalar parts of the spin-spin interaction. Vibration and rotation dependencies of these constants have been determined, allowing correction for zero point vibration effects. This experimental Cs nuclear quadrupole coupling constant when combined with the electric field gradient calculated using a relativistic coupled cluster method yields a nuclear quadrupole moment of the Cs nucleus equal to eQ= -3.43098 mbarn. The vibrational dependence of the coupling constant is smaller than the theoretical estimate. The coupling constants we have determined are the following: eQ(Cs)q(Cs) = 1245.598(10) - 14.322(25)(v + 1/2) + 0.080(14) x(v + 1/2)(2) + 0.0040(22)(v + 1/2)(3) - 0.00209(59) J(J + 1) + 0.00048(40)(v + 1/2) J(J + 1), c(Cs) = 0.66177(14) -0.01509(28)(v + 1/2) + 0.000550(94)(v + 1/2)(2), c(F) = 15.08163(84) - 0.1744(14) x (v + 1/2) +0.00234(41)(v + 1/2)(2) -0.000093(13) J(J+1), c(3) = 0.92713(53) - 0.00917(93)(v + 1/2) +0.00097(29)(v + 1/2)(2), c(4) = 0.62745(30) - 0.00903(22)(v + 1/2). All values are in kHz units, with one standard deviation uncertainty estimates in the last two digits shown in ().