Sub-theming hierarchy beyond 2 levels is broke!

A 2 level theme hierarchy works fine but add in a third and it starts to act strangely.

Testing with style sheets and it does this:

theme_a:
  stylesheets[all][] = theme-a.css

  theme_b:
    base theme = theme_a
    stylesheets[all][] = theme-b.css

    theme_c:
      base theme = theme_b
      stylesheets[all][] = theme-c.css

So, in the above example, activating theme_c, theme_a shows it's style sheet as expected but will ignore theme_b and give this error.

notice: Undefined index: theme_b in /DRUPAL-HEAD/modules/system/system.module on line 801.

That error points to system_find_base_theme().

I also looked at a var_dump of $base_theme from init_theme() and it only lists a single base theme. It should be listing both base themes.