A gate with sidechaining. There's another good technique that didn't get mentioned earlier.
I'm also wondering about the arpeggiator as an approach, although with Rapture you can design the tail off on the repeats pretty nicely.
That's the problem with using the arpeggiator. You're effectively repeating the chord notes themselves. You still need a way to provide an overall envelope for each chord change. You could do that with a repeating automation envelope, but - given all of the other techniques here - it's more work to get not-as-close.
If you want an arpeggiator starting point, try something like this:
Enable: On
Octave: 1 Octave
Shape: Rhythms Only (any Shape works in this context).
The rest at defaults.
Note that it is possible to 'embed' a velocity fade inside an .arp preset. I did some of that in the
Alesion Arp Presets project. The only way I know to create a custom core .ptn file for an .arp preset was Project5, though.
... further suggestions like this for alternative methods are welcome for sure.
I've been circling back around to the fine suggestions already given here. That 'delay' technique is certainly a viable option. You have to play staccato, and let the delay line do the heavy lifting.
I particularly like the LFO idea. You can build the amplitude and filter envelopes as if you were playing block piano chords. Then chop up the release 'tails' into segments with an AMP and/or CUT1/2 LFO. Try 7 - Saw Down or similar for an attack/decay shape like my Rapture AMP EG example above.