We present a simple theory where baryon and lepton numbers are spontaneously
broken at the supersymmetry scale. In this context R-parity must be
spontaneously broken but the theory still contains a stable field which can
play the role of the cold dark matter of the Universe. We discuss the spectrum
of the theory, the properties of the dark matter candidate and the predictions
for direct detection experiments. This theory provides a concrete example of
exotic supersymmetric signatures associated with having the simultaneous
presence of R-parity violating and missing energy signals at the Large Hadron
Collider
