The capacity of the Fast Fading Z Cognitive Inter-ference (FFZCI) channel is investigated. The FFZCI channel is a variation of the Z Gaussian cognitive interference channel in which the link between the primary transmitter and the cognitive receiver is affected by fast fading. The fast fading sequence is known at the cognitive receiver but not at the cognitive transmitter. The FFZCI channel models an underlay cognitive network in which a primary and a cognitive user attempt to communicate over the same medium: The cognitive encoder is able to acquire the primary message from the network but is unable, due to fading, to precisely estimate of the channel between the primary transmitter and the cognitive receiver. The FFZCI channel, therefore, addresses the fundamental question of the value of cognition in the presence of partial channel knowledge. For this model, we derive inner and outer bounds to capacity and provide simple conditions under which the two bounds are to within a small additive gap. The inner bound relies on a combination of rate-splitting, superposition coding, and interference pre-coding. An outer bound for the case of antipodal fading is developed through the entropy power inequality for a parameter regime in which the primary-to-cognitive interference gain is small. The inner and outer bounds are shown to be to within a small distance in a further subset of channels in which the transmit power is also sufficiently large. Although the capacity of the general channel remains unknown, our results so far suggest that a small amount of channel uncertainty is sufficient to render interference pre-cancellation of the primary interference at the cognitive receiver substantially ineffective.