  Let $k$ be a field and let $A=\bigoplus_{n\ge 1}A_n$ be a positively graded
$k$-algebra. We recall that $A$ is graded nilpotent if for every $d\ge 1$, the
subalgebra of $A$ generated by elements of degree $d$ is nilpotent. We give a
method of producing grading nilpotent algebras and use this to prove that over
any base field $k$ there exists a finitely generated graded nilpotent algebra
that contains a free $k$-subalgebra on two generators.
