We consider an asymmetric zero range process in infinite volume with zero mean and random jump rates starting from equilibrium. We investigate the large deviations from the hydrodynamical limit of the empirical distribution of particles and prove an upper and a lower bound for the large deviation principle. Our main argument is based on a super-exponential estimate in infinite volume. For this we extend to our case a method developed by Kipnis & al. (1989) and Benois & al. (1995).