We construct the exact correlation potential of Kohn-Sham density functional theory for a one-dimensional model chain of four hydrogen atoms from a highly accurate, correlated wave function. Specifically we investigate polarizabilities and the response of the correlation potential to an external linear electrical field. This model situation is of great interest to Kohn-Sham theory because it is well known that the exact Kohn-Sham exchange potential shows ultranonlocality in this situation, with the exchange potential responding opposite to the applied external potential. The results obtained here are relevant for providing guidance in the construction of improved approximate exchange correlation functionals. [Phys.Rev.A 99, 052505]