You might first check your battery connections. Sometimes, the terminals will corrode, and a good cleaning will solve the problem. Other times, they'll crack, and you'll have to replace one or both.

 

It may also be a wire to the ignition switch itself.

 

Or corrosion under the battery cable insulation at the clamp. Start by removing and cleaning battery clamps and posts, even if they look good.

Then if the problem persists, use a voltmeter to measure between the positive clamp and positive post, with headlights on. Voltage drop should not exceed about 0.3 volts, and ideally less than 0.1 volts. Repeat for the negative clamp and post. If voltage is too high, the connection between post and clamp is bad.
You can repeat this test between block and battery clamp, and starter terminal and pos battery clamp, to test the cables.

 

In addition to Bob's answer, The starter relay terminal and the firewall connector are common suspects. Some time during these years Chrysler changed to a shunt ammeter system. If you have the old 'true ammeter' system, It could be a loose/dirty ammeter terminal.

 

It could be as simple as a loose nut on one of your terminals. Make sure that the cable connections to the block, frame, and starter are also secure. Bob's suggestion about corrosion in the cables is a good one. Before you bought the car, maybe someone replaced a cable with a thinner one that isn't up to specs.

In the older Mopars, there was a place on the firewall where you could put a screwdriver between two screws to engage the starter, but you don't want to do that for very long. Someone else will have to tell you what that part is, and provide a pic, if available. I used it when setting the point gap.

 

If this affects battery-operated items (dome lights, headlamps, hazard flashers, etc), then I would look for a poor/loose connection in the battery/bulkhead (firewall) connector/dash ammeter areas.
High resistance creates heat, so if you find melted plastic or burnt wire insulation, then you have found the area.

 

Update: After my first post it happened again. This time I heard a "click" from behind the dash, left side as the power died and came back. This is a total failure so I'll have to check the firewall connector as ImperialCrown suggests.

I did notice that the battery terminal is in &^%%$ shape, so I'm going to replace it before troubleshooting further.
Thanks folks for the info thus far! Will print this off so I can have it in hand while poking around under the hood.

 

The one time I had that issue, it was the positive battery cable having a poor contact. Kinda scary when everything just dies at once, huh?