  Most massive stars, the progenitors of core-collapse supernovae, are in close
binary systems and may interact with their companion through mass transfer or
merging. We undertake a population synthesis study to compute the delay-time
distribution of core-collapse supernovae, that is, the supernova rate versus
time following a starburst, taking into account binary interactions. We test
the systematic robustness of our results by running various simulations to
account for the uncertainties in our standard assumptions. We find that a
significant fraction, $15^{+9}_{-8}$%, of core-collapse supernovae are `late',
that is, they occur 50-200 Myrs after birth, when all massive single stars have
already exploded. These late events originate predominantly from binary systems
with at least one, or, in most cases, with both stars initially being of
intermediate mass ($4-8M_{\odot}$). The main evolutionary channels that
contribute often involve either the merging of the initially more massive
primary star with its companion or the engulfment of the remaining core of the
primary by the expanding secondary that has accreted mass at an earlier
evolutionary stage. Also, the total number of core-collapse supernovae
increases by $14^{+15}_{-14}$% because of binarity for the same initial stellar
mass. The high rate implies that we should have already observed such late
core-collapse supernovae, but have not recognized them as such. We argue that
$\phi$ Persei is a likely progenitor and that eccentric neutron star - white
dwarf systems are likely descendants. Late events can help explain the
discrepancy in the delay-time distributions derived from supernova remnants in
the Magellanic Clouds and extragalactic type Ia events, lowering the
contribution of prompt Ia events. We discuss ways to test these predictions and
speculate on the implications for supernova feedback in simulations of galaxy
evolution.
