We consider materials whose mechanical integrity is the result of a jamming process. We argue that such media are generically "fragile," unable to support certain types of incremental loading without plastic rearrangement. Fragility is linked to the marginal stability of force chain networks within the material. It can lead to novel mechanical responses that may be relevant to (a) jammed collsids and (b) poured sand. The crossover from fragile to elastoplastic behavior is explored.