  In this article, we give explicit examples of maximal amenable subalgebras of
the $q$-Gaussian algebras, namely, the generator subalgebra is maximal amenable
inside the $q$-Gaussian algebras for real numbers $q$ with its absolute value
sufficiently small. To achieve this, we construct a Riesz basis in the spirit
of R\u{a}dulescu and develop a structural theorem for the $q$-Gaussian
algebras.
