Recall a graph is chordal if it contains no induced cycle of length 4 or more, and outerplanar if it has a crossing-free embedding in the plane such that all vertices are on the same face. While studying a certain problem, I came across chordal outerplanar graphs, which are graphs that are both chordal and outerplanar. ISGCI didn't know of such a class. In fact, the closest thing I was able to find was the class of chordal $\cap$ planar graphs.
Have chordal outerplanar graphs been studied before somewhere? What kind of properties do they have? Are they perhaps equivalent to some well-known (or a better known) graph class?
For example, it seems to me that every inner face of such a graph is a triangle. The motivation for the third question is that I got at most 5 hits when googling for such graphs, so I wonder if such graphs might be commonly known as something other than chordal outerplanar graphs.