Fault diagnosis consists in synthesizing a diagnoser that observes a given plant through a set of observable events, and identifies faults which are not observable as soon as possible after their occurrence. Existing literature on this problem has considered the case of static observers, where the set of observable events does not change during exe- cution of the system. In this paper, we consider dynamic observers, where the observer can switch sensors on or off, thus dynamically changing the set of events it wishes to observe. We define a notion of cost for such dynamic observers and show that (i) the cost of a given dynamic observer can be computed and (ii) an optimal dynamic observer can be synthesized.