You don't need to "narrate" your thoughts. This is generally called sub-vocalization, where you actually associate a word with a concept. It is generally believed that people subvocalize exclusively in their native language without a lot of training (like nate said), but that doesn't mean you have to subvocalize at all.
Silencing the "inner voice" can lead to much faster thought processing. For instance, it removes the need to communicate with the Broca's area of the brain. People who are training to speed read are training to remove sub-vocalization; instead, they can read text and simply interpret what the words mean without using standard language as a medium. Yes, they are still reading in a given language, but that doesn't mean their brain is understanding it directly as a language. You can train to do this same thing with thought, and most people already do on a subconscious level.
For some anecdotal evidence, I have learned to process thoughts without subvocalization, but that doesn't mean it's always. For instance, one time I was at a museum watching a production on some feature they had. The lady behind me was translating it to her daughter in spanish. After a few minutes I realize I had stopped listening to the movie and was relying on her translation instead. I'm not an expert, so I don't know if I was subvocalizing the Spanish or just picking up on the language because a second language is actually stored in other parts of your brain than your native tongue is. Anyway, it was kind of cool to realize what was happening, though I'm not sure if it answers the question at all...
