First off, like most respondents here point out, if the guy doesn't see the value in testing, there's not much you can do about it, and you've already pointed out that you can't fire the guy. However, failure is not an option here, so what about the few things you can do?
If your organization is large enough to have over 6 developers, I strongly recommend having a Quality Assurance department (even if its just one person to start). Ideally, you should have a ratio of 1 tester to 3-5 developers. The thing about programmers is ... they are programmers, not testers. I have yet to interview a programmer that has been formally taught proper QA techniques.
Most organizations make the fatal flaw of assigning the testing roles to the new-hire, the person with the LEAST amount of exposure to your code -- ideally, the senior developers should be moved to the QA role as they have the experience in the code, and (hopefully) have developed a sixth sense for code smells and failure points that can crop up.
Furthermore, the programmer that made the mistake is probably not going to find the defect because its usually not a syntax error (those get picked up in the compile), but a logic error -- and the same logic is at work when they write the test as when they write the code. Don't have the person who developed the code test that code -- they'll find less bugs than anyone else would.
In your case, if you can afford the redirected work effort, make this new guy the first member of your QA team. Get him to read "Software Testing In The Real World: Improving The Process", because he obviously will need some training in his new role. If he doesn't like it, he'll quit and your problem is still solved.
A slightly less vengeful approach would be let this person do what they are good at (I'm assuming this person got hired because they are actually competent at the programming part of the job) , and hire a tester or two to do the testing (University students often have practicum or "co-op" terms, would love the exposure, and are cheap)
Side Note: Eventually, you'll want the QA team reporting to a QA director, or at least not to a software developer manager, because having the QA team report to the manager who's primary goal is to get the product done is a conflict of interest.
If your organization is smaller than 6, or you can't get away with creating a new team, I recommend paired programming (PP). I'm not a total convert of all the extreme programming techniques, but I'm definitely a believer in paired programming. However, both members of the paired programming team have to be dedicated, or it simply doesn't work. They have to follow two rules: the inspector has to fully understand what is being coded on the screen or he has to ask the coder to explain it; the coder can only code what he can explain -- no "you'll see" or "trust me" or hand-waving will be tolerated.
I only recommend PP if your team is capable of it, because, like testing, no amount of cheering or threatening will persuade a couple of ego-filled introverts to work together if they don't feel comfortable doing so. However, I find that between the choice of writing detailed functional specs and doing code reviews vs. paired programming, the PP usually wins out.
If PP is not for you, then TDD is your best bet, but only if its taken literally. Test Driven Development mean you write the tests FIRST, run the tests to prove they actually do fail, then write the simplest code to make it work. The trade off is now you (should) have a collection of thousands of tests, which is also code, and is just as likely as production code to contain bugs. I'll be honest, I'm not a big fan of TDD, mainly because of this reason, but it works for many developers who would rather write test scripts than test case documents -- some testing is better than none. Couple TDD with PP for a better likelihood of test coverage and less bugs in the script.
If all else fails, have the programmers equivalence of a swear jar -- each time the programmer breaks the build, they have to put $20, $50, $100 (whatever is moderately painful for your staff) into a jar that goes to your favorite (registered!) charity. Until they pay up, shun them :)
All joking aside, the best way to get your programmer to write tests is don't let him program. If you want a programmer, hire a programmer -- If you want tests, hire a tester. I started as a junior programmer 12 years ago doing testing, and it turned into my career path, and I wouldn't trade it for anything. A solid QA department that is properly nurtured and given the power and mandate to improve the software is just as valuable as the developers writing the software in the first place.