The other day on the Absolute Write forum, I ran across a discussion asking whether it's okay to open a story with dialogue.
Let me say this first: most things in writing can be done. Some will say the real question is whether they can be done well, but I'm going to disagree with that. The question for me is what exactly one accomplishes by starting with a line of dialogue. Not whether you can do it, but what you are accomplishing by doing it.
When I'm opening a story or a chapter or a scene, I'll often think of a line of dialogue first. By the time I'm finished, though, it seldom ends up at the front. Most of the time I'm trying to make sure that my opening is doing a few things: establishing the voice and psychology of the point of view character, anchoring readers in the conflict that's going on, and making them curious. I like to provide grounding information which allows readers to put their feet down (so to speak) so they can then follow me through the rest of the piece. It's possible to put some grounding information in a line of dialogue, but too much will make the dialogue itself seem stilted and odd.
When your story opens with a line of dialogue, what you're really doing is letting your reader listen to someone speaking. You may or may not, at the same time, be indicating who that person is. It's enticing as an opener because it does usually make people curious (depending, of course, on what is being said). If the dialogue continues without other elements of narrative, however, a sense of disorientation will persist.
This is not necessarily a problem. However, you will have to ask yourself: do I want readers to be disoriented?
You might. If you're having a character waking up from a state of unconsciousness, or someone in a state of confusion without a clear sense of physical orientation, it might work. Alternately, if you're letting the reader eavesdrop on nefarious yet unidentifiable bad guys, it might be a good idea. Clearly, there are workable scenarios.
The book Ender's Game opens with a lengthy conversation between two people, and it works very well. It's effective in part because the dialogue is not delivered by the protagonist, but is speaking about the protagonist. If the author had chosen to ground the two speakers in a physical location, the immediate assumption would be that they were the protagonists; clearly they are not. The way the opening dialogue is handled opens both curiosity and the main conflict (the secret controllers of Ender's life) while keeping the focus of the story where it needs to be - on Ender. It's like those movies where they give you a sense that someone is being watched by picking particular camera angles.
It's also possible to begin with a single line of dialogue (maybe two?) and then follow it with orientation information. If the curiosity established by the opening sentence is sufficient, grounding can be provided in the second or third sentence.
As always, you have to assess these things as you go, on the basis of what you're trying to accomplish. I hope these thoughts help clarify some of the variables involved in making the decision whether to open a story, scene, or chapter with dialogue.