  We consider physics beyond the Standard Model in which a long-lived
electromagnetically charged massive particle species (CHAMP) appears. We
discuss the unique sensitivity the early Universe exhibits on the mere presence
and on the decay of such a particle. A CHAMP can be realized in supersymmetric
extensions of the Standard Model. We carry out a detailed study of gravitino
dark matter scenarios in which the lighter stau is the lightest Standard Model
superpartner and thus the CHAMP. Particularly stringent constraints on the
gravitino-stau scenario arise from the thermal catalysis of primordial
nucleosynthesis reactions. This motivates a thorough investigation of the
thermal freeze-out process of the long-lived stau. There, we show that even the
most stringent cosmological constraints can potentially be evaded.
