<p>I am trying to use a DynamicResource in Storyboard contained within a ControlTemplate.</p>

<p>But, when I try to do this, I get a 'Cannot freeze this Storyboard timeline tree for use across threads' error.</p>

<p>What is going on here?</p>

No, you can't use a DynamicResource in a Storyboard that is contained within a Style or ControlTemplate. In fact, you can't use a data binding expression either.
The story here is that everything within a Style or ControlTemplate must be safe for use across threads and the timing system actually tries to freeze the Style or ControlTemplate to make them thread-safe. However, if a DynamicResource or data binding expression is present, it is unable to freeze them.
For more info see:
MSDN Link
. Check out the 'Animate in a Style' and the 'Animate in a ControlTemplate' sections (this documentation page is rather long).
And for a workaround (at least for my scenario) see:
WPF Forum Post
.
Hope this helps someone. I've lost more than enough hair on it.
Cory