  The zero-error feedback capacity of the Gelfand-Pinsker channel is
established. It can be positive even if the channel's zero-error capacity is
zero in the absence of feedback. Moreover, the error-free transmission of a
single bit may require more than one channel use. These phenomena do not occur
when the state is revealed to the transmitter causally, a case that is solved
here using Shannon strategies. Cost constraints on the channel inputs or
channel states are also discussed, as is the scenario where---in addition to
the message---also the state sequence must be recovered.
