  A Semmes surface in the Heisenberg group is a closed set $S$ that is upper
Ahlfors-regular with codimension one and satisfies the following condition,
referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r <
\operatorname{diam} S$ contains two balls with radii comparable to $r$ which
are contained in different connected components of the complement of $S$.
Analogous sets in Euclidean spaces were introduced by Semmes in the late
$80$'s. We prove that Semmes surfaces in the Heisenberg group are lower
Ahlfors-regular with codimension one and have big pieces of intrinsic Lipschitz
graphs. In particular, our result applies to the boundary of chord-arc domains
and of reduced isoperimetric sets.
