  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.
