We study the Hall effect in a system of weakly coupled Luttinger Liquid chains, using a Memory function approach to compute the Hall constant in the presence of umklapp scattering along the chains. In this approximation, the Hall constant decomposes into two terms: a high-frequency term and a Memory function term. For the case of zero umklapp scattering, where the Memory function vanishes, the Hall constant is simply the band value, in agreement with former results in a similar model with no dissipation along the chains. With umklapp scattering along the chains, we find a power-law temperature dependance of the Hall constant. We discuss the applications to quasi 1D organic conductors at high temperatures.