The nuclear quadrupole moment (NQM) of the 133 isotope of Cs is not accurately known. This is due to the fact that the electric field gradient (EFG) of Ca for the 6p(1 2)P(3/2) excited state was only estimated from the 6p(r(-3)) expectation value using Hartree-Slater calculations. CsF microwave data yield a very accurate nuclear quadrupole coupling constant (NQCC). We therefore decided to perform relativistic coupled cluster calculations for CsF in order to obtain a more accurate value for the Cs EFG. At the highest level of theory we obtain a NQM for the first vibrational-rotational state of -3.43(10) mb which should be more accurate than the previously estimated value of -3.7(1.6) mb or -9(4) mb.