When I replied, I was under the impression that the poster was asking about leaving the driver's door open. I now see that he probably wants to have any, or all, doors open without hearing the chime.
It's more work, but it still has to be done by spoofing each door ajar sensor, as the chime is integrated into the instrument cluster, and can't be easily disabled on it's own. In this case, one could obtain all four wires at the instrument cluster connector.
To remove the instrument cluster, remove the two screws that hold the cluster bezel in place. These are on the underside of the bezel, and you'll need a short, stubby phillips to get them out. Once the bezel is removed, four screws hold the cluster in place. Pull the cluster forward, and disconnect the electrical connectors.
Of the three cluster connectors, you're looking for the 26-pin gray connector. Pins 1-4 are the four door sense circuits (1 - violet, driver's door 2 - violet/gray, left rear door 3 - violet/yellow, right rear door
4 - violet/white, right rear door).
Again, depending on the operation of the door latch, you'll either need to tap into all four wires and switch them to ground, or cut all four wires and insert a switch into the electrical path. My guess would be that the circuits are grounded when the door is closed, but double-check just in case.
If they are grounded when the door is closed, resist the temptation to just tap all four to the same SPST switch. You'll disable you door ajar sensors completely this way, unless all four are opened. You need to use a 4-pole switch (probably need to go to an electrical supply place for this - not something Radio Shack would carry).