  Zigzags in graphs embedded in surfaces are cyclic sequences of edges whose
any two consecutive edges are different, have a common vertex and belong to the
same face. We investigate zigzags in randomly constructed combinatorial
tetrahedral chains. Every such chain contains at most $3$ zigzags up to
reversing. The main result is the limit of the probability that a randomly
constructed tetrahedral chain contains precisely $k\in\{1,2,3\}$ zigzags up to
reversing as its length approaches infinity. Our key tool is the Markov chain
whose states are types of $z$-monodromies.
