  The random Fibonacci chain is a generalisation of the classical Fibonacci
substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 01$
with probability $p$ and $1 \mapsto 10$ with probability $1-p$ for $0<p<1$ and
where the random rule is applied each time it acts on a 1. We show that the
topological entropy of this object is given by the growth rate of the set of
inflated random Fibonacci words.
