  We propose a new definition of "horizon molecules" in Causal Set Theory
following pioneering work by Dou and Sorkin. The new concept applies for any
causal horizon and its intersection with any spacelike hypersurface. In the
continuum limit, as the discreteness scale tends to zero, the leading behaviour
of the expected number of horizon molecules is shown to be the area of the
horizon in discreteness units, up to a dimension dependent factor of order one.
We also determine the first order corrections to the continuum value, and show
how such corrections can be exploited to obtain further geometrical information
about the horizon and the spacelike hypersurface from the causal set.
