Make sure your lights are off, although the 03 Accord has Auto-Off lights, which I leave on most of the time, it does chime when you open the door. Thats the only chime I have noticed with my 03 V6 Coupe.

 

accord ex-v6 needs auto-on light feature

 

:werd:

 

I doubt the chiming is the alarm, as someone said it coincides with the blinking of the instrument panel. eh, i never let it bother me.

 

AwSoMNaMjA had it right, it was the alarm. Thanks.

 

I've never noticed it on mine.

 

Well I did find a way to test out the alarm, although i don't think I can re-enact it.
I was showing my friend my car, so I had him sit in my car, closed the door. Then I lowered the windows with the remote. A few seconds after, the doors locked while I was talking to my friend. Then I told him to put the key in and turn it so he could put the windows back up. The ACC position wasnt enuf, so I had em turn it to ON and once he did that the instrumentation lit up and the alarm started going off and he freaked, so I had to get the keys back and press the unlock button.
First I figured maybe he hit the panic button, but the guide says to turn the ignition to ON to stop panic mode and that the panic mode won't work with the ignition ON.