I'm going to disagree with everyone so far. I think you should close the newest one. (You can always reopen it again and they will usually give you the discount.)
1. A large part of your credit score is based on how long your accounts have been open. The longer the card has been open the more history you have.
2. Since you don't carry a balance on the card, it makes your debt ratio look smaller. You may have $15,000 limit with all the cards combined. If you carry $5000 worth of debt, you ratio is 1/3. But if you close the cards and your total credit limit drops to $10,000, with $5,000 still. Your debt is now 1/2. The smaller the debt ratio, the better you will look if you're buying something big, such as a house. (After you get the mortgage, then close accounts). Too much debt can hurt you, like Pennypincher was saying, so be reasonable.
3. Not that checking your credit score isn't good, but too many times can actually hurt you. A potential lender will see this as a sign you are going to open more credit accounts. I think you can get purchase a set time in which you can monitor your credit. If you purchased it online, I think you can use their calculator to estimate your new score if you close a card, pay off a card, pay on time, etc.
A side note. I know someone that had their identity stolen. She had opened up a department store card years ago at Target, and had never closed the account. The thief then tried to open a card there and was denied. This happened at 1-2 more places, and all because she had the cards still open.
Do some more research about it before you decide which one to close. A couple of good websites are:
http://www.bankrate.com/brm/credit_scoring_home.asp and kiplinger.com among others.