Chordal Graph.
A chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle.
Hamiltonian Graph.
If there exists a closed walk in the connected graph that visits every vertex of the graph exactly once (except starting vertex) without repeating the edges, then such a graph is called as a Hamiltonian graph.
Based on these definitions, I suppose the following definition of Hamiltonian Chordal graph.
Hamiltonian Chordal Graph.
A graph that satisfies all the properties of Hamiltonian graph and Chordal graph.
Note.
The graph under consideration are simple and undirected.