  The long standing anomaly in the positron flux as measured by the PAMELA and
AMS-02 experiments could potentially be explained by dark matter (DM)
annihilations. This scenario typically requires a large "boost factor" to be
consistent with a thermal relic dark matter candidate produced via freeze-out.
However, such an explanation is disfavored by constraints from CMB observations
on energy deposition during the epoch of recombination. We discuss a scenario
called late-decaying two-component dark matter (LD2DM), where the entire DM
consists of two semi-degenerate species. Within this framework, the heavier
species is produced as a thermal relic in the early universe and decays to the
lighter species over cosmological timescales. Consequently, the lighter species
becomes the DM which populates the universe today. We show that annihilation of
the lighter DM species with an enhanced cross-section, produced via such a
non-thermal mechanism, can explain the observed AMS-02 positron flux while
avoiding CMB constraints. The observed DM relic density can be correctly
reproduced as well with simple s-wave annihilation cross-sections. We
demonstrate that the scenario is safe from CMB constraints on late-time energy
depositions during the cosmic "dark ages". Interestingly, structure formation
constraints force us to consider small mass splittings between the two dark
matter species. We explore possible cosmological and particle physics
signatures in a toy model that realizes this scenario.
