I've been battling over whether to have an introduction to my memoirs, and in the end I decided to do it. Battling because the general consensus seems to be that agents and publishers don't like introductions. For me I just couldn't make the strict chronological format that I wanted work without an introduction, but (thanks to good advice from AWers) I've made dam sure the intro is one of the most exciting and interesting bits of the whole book, and (I hope) the background-setting that simply had to be done slips in almost entirely unnoticed.
Much of the intro-vs.-no intro and prologue-vs.-no-prologue debate on the AW boards challenges intros / prologues heavily, because (people say) they often end up being either non-essential and/or info dump sites. And usually the question is "Are you really sure you need an intro? Can't you get that info weaved in elsewhere? And if you really really can't, you'd better make sure it's a seriously exciting / interesting intro that's going to hook that agent as well as, if not better than, your Chapter 1."
So. Where am I going with this. If you agree with all the above, then your question might be a neat little test for yourself. If you think you can get away with sending the first three chapters and not your intro, then that might suggest your intro is not quite so essential as all that, and you should be getting rid of it anyway.
If you're still convinced your intro is essential, then surely you must send it, because as wax_and_wick says, the rest doesn't make sense without it.
And if you know you want to send it because the three chapters don't make sense without it, but you're reluctant to do so because you like the idea of hitting the agent / publisher with your ultra-gripping Chapter 1 instead, then maybe your intro needs more work. I know I had that realisation at one point...
I could be way off the mark with all that. You may be in a totally different situation. But it just struck me that in my position, having ummed and aahed over an intro for so long, it's inconceivable that I wouldn't send it (for all the reasons above). Even though it goes against the letter of what the agent asked for.
Cheers