Historical Support for Singular 'They'
If you are a respected editor in charge of writing a style guide for your organization, you can get away with making it acceptable to use they with a singular antecedent. I would even encourage you to do so, and there are a variety of credible references that will back you up including the Random House Dictionary and Fowler's Modern English Usage. You would be in the company of revered authors such as Jane Austen, Lewis Carroll, and Shakespeare. I applaud Bill Walsh for making the singular they acceptable at the Post, and I encourage others to follow his lead.
But, if you are at a more conservative publication and are responsible to superiors, there's still a good chance that at least one of them will think you are careless or ignorant or at least a rebel if you use the singular they. If I were writing for a business client who didn’t have a style guide, I would still always avoid the singular they.
Write a Style Guide Entry
And that brings me to an important point: everyone who hires writers or assigns writing needs to have a style guide entry on this topic. Writers can waste a lot of time trying to decide what to do (especially in organizations where people collaborate on documents), and it is better to have one single style that some people don't agree with than to have different writers doing different things so that company documents are all willy-nilly.
So here's the bottom line: Rewrite your sentences to avoid the problem. If that's not possible, check to see if the people you are writing for have a style guide. If not, use he or she if you must, or use they if you feel bold, secure, and are prepared to defend yourself.
Get more tips like this in Grammar Girl's 101 Troublesome Words You'll Master in No Time: