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In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycleextendible; that is, the vertices of any non-Hamiltonian cycle are contained ina cycle of length one greater. We disprove this conjecture by constructingcounterexamples on $n$ vertices for any $n \geq 15$. Furthermore, we show thatthere exist counterexamples where the ratio of the length of a non-extendiblecycle to the total number of vertices can be made arbitrarily small. We thenconsider cycle extendibility in Hamiltonian chordal graphs where certaininduced subgraphs are forbidden, notably $P_n$ and the bull.

Hamiltonian chordal graphs are not cycle extendible