I have just proudly purchased a pt cruiser and it's something
I've wanted to do for a long time. I drove it for about 2 weeks without a problem. Then yesterday, I was parked
at Walmart and as soon as I put the key into the door
lock, the alarm system went off with lights a-flashing and
horn blowing. Now considering I never received a key less
remote button when I purchased the car, it was an embarrassment to me. People all staring . The car dealer
said he didn't even know the thing had an alarm, will
now order me one. Well it happens every time I unlock
the doors. Is there a way of disarming this thing, it's
become a nuisance.

 

Those car alarms usually arm when you lock the doors with the electric door lock switch in the car. They also arm when you lock the doors with the remote, but you obviously don't have one so that's not the problem.
The system usually does not arm if you lock the doors with the mechanical door lock button on the window ledge.
You car may be different, but try experimenting by using the mechanical rather than the electrical lock. You probably have a light on the dash that flashes while the system is arming (during a period of about 30 seconds after you lock the car with the electrical switch) and then flashes more slowly when the system is armed.
If the light is not flashing at all, then the system isn't armed. In that case, it shouldn't go nuts when you open the door. Of course, it won't make a peep if somebody breaks in either.
Once you get the remote, you should be able to properly control the system. Read your owners manual for details on how the system is supposed to work. If you don't have an owners manual, you may be able to find one on eBay, or try chrysler.com.