Yes, my daily driver is a Neon. Check the #1 and #2 spark plug. Could be the plug, or wire. In my case, the tube around the plug had worked loose and was letting oil fill the tube, shorting out the plug.
The neons have a very sensitive routine in the engine computer to check for misfires, sensitive enough to trip for even a minor miss on startup. As Bill suggested take a look at the wires and down where the plug is to be sure there is no oil present. Often times it is a sign that to change the plugs although the factory wires typically are good for 100K plus miles.
If no problem is found with the plugs/wires, check the coil-pack.
I had the coil-pack on a customer's Neon that would throw a mis-fire code. Very intermitted, then got worse over a 6 month period. If you don't have the tools/knowledge, most AutoZones will check the coil-pack for free.
Also remember that if it's a DOHC, they are known to do that from time to time, particularly if you let them sit. Just mentioning it so that you don't go chasing your tail on it, replacing everything to no avail, like a friend of mine did on his R/T.
To add on to what the other Matt mentioned, I'd suggest NGK plugs. Seems to reduce the misfire issue. No eliminate it, but reduce it