Interactions of a₂,K*₂,f₂ and f₂′ tensor-mesons with low-energy π,K,η,η′ pseudo-scalar mesons are constrained by chiral symmetry. We derive a chiral Lagrangian of tensor mesons in which the tensor mesons are treated as heavy non-relativistic matter fields. Using 1/N_c counting, we derive relations among unknown couplings of the chiral Lagrangian. Chiral perturbation theory is applied to the tensor-meson mass matrix. At one-loop there are large corrections to the individual tensor meson masses, but the singlet-octet mixing angle remains almost unchanged. We argue that all heavy mesons of spin ≥ 1 share common feature of chiral dynamics.