  Let $u \shuffle v$ denote the set of all shuffles of the words $u$ and $v$.
It is shown that for each integer $n \geq 3$ there exists a square-free ternary
word $u$ of length $n$ such that $u\shuffle u$ contains a square-free word.
This property is then shown to also hold for infinite words, i.e., there exists
an infinite square-free word $u$ on three letters such that $u$ can be shuffled
with itself to produce an infinite square-free word $w \in u \shuffle u$.
