  We prove that the finitely generated simple left orderable groups constructed
by the second author with Hyde have vanishing second bounded cohomology, both
with trivial real and trivial integral coefficients. As a consequence, these
are the first examples of finitely generated non-indicable left orderable
groups with vanishing second bounded cohomology. This answers Question 8 from
the 2018 ICM proceedings article of Andr\'es Navas.
