The response of polar nanoregions (PNR) in the relaxor compound Pb[(Zn$_{1/3}$Nb$_{2/3}$)$_{0.92}$Ti$_{0.08}$]O$_3$ subject to a [111]-oriented electric field has been studied by neutron diffuse scattering. Contrary to classical expectations, the diffuse scattering associated with the PNR persists, and is even partially enhanced by field cooling. The effect of the external electric field is retained by the PNR after the field is removed. The ``memory of the applied field reappears even after heating the system above $T_C$, and cooling in zero field.
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