Every circle graph of girth at least 5 is 3-colourable

It is known that every triangle-free (equivalently, of girth at least 4) circle graph is 5-colourable (Kostochka, 1988) and that there exist examples of these graphs which are not 4-colourable (Ageev, 1996). In this note we show that every circle graph of girth at least 5 is 2-degenerate and, consequently, not only 3-colourable but even 3-choosable.