We show that the Fe (VII-XII) M-shell unresolved transition array (UTA) in the NGC 3783 900 ks Chandra HETGS observation clearly changes in opacity in a timescale of 31 days responding to a factor of 2 change in the ionizing continuum. The opacity variation is observed at a level >10 sigma. There is also evidence for variability in the O VI K edge (at 3 sigma level). The observed changes are consistent with the gas producing these absorption features (the low ionization component) being close to photoionization equilibrium. The gas responsible for the Fe (XVII-XXII) L-shell absorption (the high ionization component), does not seem to be responding as expected in photoionization equilibrium. The observed change in opacity for the UTA implies a density >1E4 cm-3, and so locates the gas within 6 pc of the X-ray source. The scenario in which the gas is composed of a continuous radial range of ionization structures is ruled out, as in such scenario, no opacity variations are expected. Rather, the structure of the absorber is likely composed by heavily clumped gas.