Hydrogen does bond to chlorine. This is the case in HCl, a very corrosive gas that dissolves readily in water forming hydrochloric acid. HCl doesn't exhibit hydrogen bonding, because as stated earlier, the chlorine atom is too big, and the hydrogen atom does not feel an immense pull by the chlorine's nucleus. As a result, it doesn't have a very strong delta plus charge. The bond is considered polar covalent, but the HCl molecule does not exhibit hydrogen bonding. The reason why only N, O, and F are classified as hydrogen bond formers is that they have a fairly high electronegativity compared to hydrogen, and none of them have a great deal of electrons shielding their nucleus. As a result, the electron on the hydrogen atom is able to feel the pull of the N, O, and F's nucleus which creates a slight positive charge.