The ALICE data on light flavor hadron production obtained in $p-Pb$ collisions at $sqrt{s_{NN}} $ = 5.02 TeV are studied in the thermal model using the canonical approach with exact strangeness conservation. The chemical freeze-out temperature is independent of centrality except for the lowest multiplicity bin, with values close to 160 MeV but consistent with those obtained in $Pb-Pb$ collisions at $sqrt{s_{NN}}$ = 2.76 TeV. The value of the strangeness non-equilibrium factor $gamma_s$ is slowly increasing with multiplicity from 0.9 to 0.96, i.e. it is always very close to full chemical equilibrium.