Depends on the transmission. Assuming its Torqueflite 727, 904 or variant then a Dex III replacement is backward compatible.
The needs of all Chrysler transmissions are not the same. There are long articles on this (go to Allpar.com for an example). The big change in Chrysler ATF was the development of ATF+3 and +4 for the new transmissions with control modules. Therefore my conclusion has been that bottle labelled compatible with ALL Chrysler transmissions is a bad sign.
That said, many ATFs are backward compatible. Chrysler changed recommendations as fluid improved. Each newer specification for ATFs usually resulted in better oxidation resistance and low temperature viscosity.
My suggestion for accepting or rejecting a newer ATF as substitute for an earlier one like Type A or Dexron II is to see if the manufacturer specifically makes that assertion. In other words it says "replacement for Dexron II" or something like that on the spec sheet (often available on line) or bottle.
My own generalized list for Dex II replacement is as follows:Dexron VI (synthetic and generally most expensive)
Synthetic Dexron spec'd as Dex III replacement
Dexron/Mercon (least expensive)
Multi-purpose (usually least expensive, but IMO these are a crap shoot on compatibility)
An earlier thread where pros and cons of various ATFs have were discussed.
727 fluid - What to use? 
