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. 1 arXiv:1909.08620v1 [gr-qc] 18 Sep 2019 7 Entropy 31 Appendices 32 A I − (M − + ) ∩ M − − = I − (J ) 32 B Determining the set of independent scalars 32 8 References 36 a (d) H to get an estimate for the horizon area of a causal set. In the continuum limit the expectation value of the associated random variable was the horizon area, which is proportional to the first term in the small l expansion of J dV J I (d) 1 (q; l, τ ) = a (d) n J dV J + l J dV J b