Welcome to the wonderful world of negotiation, where every candidate seems to have attended a class on effective negotiation.  I'll spare you the regular discourse on how badly you need the talent (and whether you are going to find another suitable candidate) and get right to the issue - what do you do when a candidate counters?  Once a candidate presents you with a counteroffer to your original offer, you basically have four choices:

1.  Accept their Counteroffer and close the deal - this probably means you low-balled them initially or the skill set is so critical you can't delay the hire - so after giving it the "old college try" to keep the offer down, you'll crumble like a deck of cards built on sand....

2.  Give a Little Ground and Go Back to the Candidate with a Counteroffer of your own somewhere in the middle - a common practice, which usually shows that both parties are expecting some process to get to a number they are comfortable with.  Nobody goes on the car lot without expecting to haggle a little bit, right?

3.  Hold Firm on the Offer that was originally made - you love the candidate but aren't going to budge.  Tell them you love them, but the offer is the offer.  Always helps to have some reasons why - budget, salary range guidelines, your view of the marketplace, other candidates in th mix you can go to, etc...

4.  Walk Away Cold - The hardcore reaction to a counteroffer, this action means that once the candidate counters, you are retracting your initial offer and letting them know no counter offer will be forthcoming from the company.  I see this happen the most when the company has done everything it needs to measure the compensation needs of the candidate (This usually means you ask them! What a novel approach!), then the candidate surprises them by asking for more after indicating an offer along the lines of the one made would be acceptable.  That can create a trust issue that can't be overcome.  Additionally, sometimes the hiring manager won't want to work through the process, preferring instead to simply walk away.

I know - walking away cold seems harsh doesn't it?  In our experience, #2 is the most common, followed by #3.  #1 happens less, and as we outlined, #4 is generally only used if someone gets their feelings hurt.

It's more art than science.  Good luck out there...