For H bonding to take place, HOMO of halogen containing compound will involve in bond formation (in other words reaction) with LUMO of H. For F, N and O we observe that there is no orbital mismatch and the energy differences are quite small and thus can lead to easy H bonding. However, when it comes to Cl we should appreciate the orbital mismatch taking place. Look at how much energy gap will occur. Thus H bonding can take place in very rare crystal structures for chlorine. It is possible and that is why if you refer to Sudarshan Guha adapted version for JD Lee he would have mentioned N, O, F and Cl are involved in H bonding (I guess he forgot to remove it). Check this under hydrogen chapter. Also there are examples given under H bonding that highlight organic compounds containing Cl Hydrogen bond
One of my friends had sent me this text once.
I hope he doesn't mind if he reads it.