The dealer has a tool, called a VATS (vehicle anti-theft system) interrogator. It is used to simulate the 15 different values of the key "chip" which is really just a resistor. They can hook this up to determine the correct value for your car, but it is a kind of stupid process, as they have to go through each value starting from the first until the hit the right one.
If you have the 15th one for example , they have to do the procedure 15 times, waiting 4 minutes each time for the lockout to expire before they try the next one, thus it can be time consuming (and that equals $).
You cannot have the wrong value or it would never work as has already been pointed out, BUT I have seen the resistor pellets go bad, especially in non-GM genuine key blanks.
I had a cheap one a locksmith made for me, worked for about a year then started getting intermittent "wait 3 minutes" lockouts. My other keys always worked fine, so I tested the faulty one with an ohmmeter and found the value had drifted well out of spec. This may be your problem.
You may also have a dirty (oxidized) contact on the pellet (can be cleaned with a pencil eraser on both sides) or in the key switch (which is basically impossible to clean, maybe a q-tip with some rubbing alchohol could get in there far enough to clean in). Other possiblities include poor mechincal contact in the key switch (due to wear) or itermittent open in the wiring (which is very thin and is known to break eventually) both of which requrie replacement of the iginition key switch asembly.
Finally, the PASS-key module (the part that controls/interprets the key chip) could be faulty, but this is a rather uncommon failure point.
I would first check the key to make sure it isn't dirty or has drifted off it's correct resistance. If it has, see if the locksmith who made the key or the dealer knows what value it was and have them make a new one.
Otherwise, you're looking at spending some bucks.
KDirk