Broken theme – template missing

I’m running the 2004-12-19 nightly and have a theme consisting of css file plus index.php installed in the appropriate directory (according to the manual in the Codex). Under the presentation tab in wp-admin, this theme shows as “broken”. Its name links to https://mysiteurl/wp-admin/mysiteurl (which is nonsense, of course), and its “description” reads “Template is missing.”
I wonder, what kind of template is missing? The manual says it’s enough for a theme to have just css and index, which is what I have.