No. There are basically two parts to your code that you want to protect: the algorithms and the copyright. If your hosting provider's terms of service are anything resembling sane, then keeping your code on their site isn't doing anything to compromise the copyright, and anyone willing to steal your code outright in manner that violates the copyright isn't your competition.

Most applications don't use or require any algorithms sufficiently innovative to be worth protecting. If you're in the minority, then you should be a lot more concerned about your former employees than your hosting provider. It might be worth getting a patent, but really the odds of having your ideas stolen by your hosting provider and then sold to competition and having this result in a meaningful loss to your company are probably orders of magnitude smaller than your odds of getting struck by lightning.

Encrypt it. There are lots of open source programs that can do that for you. Even if they get a hold of the files they will be meaningless without your private key.

If he's talking about interpreted server-side code that's not very realistic. The third party has total physical access to the machine. It's pretty hard to have the code run and remain encrypted at all times -- impossible in most cases. The closest real thing you can do is obfuscate your code, which can make things painful for you as well.

If you're a US company and the third party is as well I'd just rely on copyright law for protection. If they're a foreign company it's more difficult.

Concerned why? Are you concerned about someone stealing your proprietary code?

Or are you worried because you have made unreleased proprietary modifications to GPLed code and you are worried that running your modified version on another parties servers might be considered "distribution," and give the host the option of distributing it to other parties?

Don't worry, they probably couldn't understand the code anyway even if their ethics lapsed.

Make sure to obfuscate your Javascript/CSS files.