We analyze two X-shooter spectra of the GRB 120327A afterglow, acquired    2.1 and    30 hrs after the trigger. The ISM in the GRB host galaxy at z = 2.8145 is extremely rich in absorption features, with three components contributing to the line profiles. The hydrogen column density associated with GRB 120327A is log NHI / cm2 = 22.01 ± 0.09, and the metallicity of the host galaxy is in the range [X/H] =  − 1.7 to  − 1 with respect to the solar values, i.e., a typical value for a GRB host galaxy. In addition to the ground state lines, we detect in the first observation several excited absorption features, which disappeared in the second observation. Using these features, we derive that component I is at dI = 200+100-60 pc from the GRB, while component II is located closer, at dII = 100+4030 pc. These values are among the lowest found in GRBs. Comparing the abundances with star formation history models, we find that the GRB 120327A host galaxy abundances are compatible with a star formation efficiency of 10 Gyr-1, typical of spheroids (elliptical or bulge).