  We answer a question of Calkin and Wilf concerning the maximal order of
Stern's diatomic sequence. Specifically, we prove that
$$\limsup_{n\to\infty}\frac{a(n)}{\varphi^{\log_2 n}}=\frac{\varphi^{\log_2
3}}{\sqrt{5}},$$ where $\varphi=(\sqrt{5}+1)/2$ is the golden ratio. This
improves on previous results given by Berlekamp, Conway, and Guy, who showed
that the limit value was bounded above by 1.25, and by Calkin and Wilf, who
showed that the exact value was in the interval
$[({\varphi}/{\sqrt{5}})({3}/{2})^{\log_2\varphi},(\varphi+1)/{\sqrt{5}}].$
