What effect stabilizes chaos by randomness? Reading the book Antifragile-Nassim Nicholas Taleb, I encountered the following paragraph.

And ironically, the so-called chaotic systems, those experiencing a brand of variations called chaos, can be stabilized by adding randomness to them. I watched the eerie demonstration of the effects, presented by a doctoral student who first got balls to jump chaotically on a table in response to steady vibrations on the surface. These steady chocks made the balls jump in a jumbled and inelegand manner. Then, as by magic, he moved a switch and the jumps became orderly and smooth. The magic is that such change of regime, from chaos to order, did not take place by removing chaos, but by adding random, completely random but low-intensity shocks. I came out of the beautiful experiment with so much enthusiasm that I wanted to inform strangers on the street, "I love randomness!"

It is the first time I've heard of this effect, does it have a name and is it properly understood? 
 A: This sounds like stochastic resonance.
From Scholarpedia on stochastic resonance:

Broadly speaking, stochastic resonance is a mechanism by which a system embedded in a noisy environment acquires an enhanced sensitivity towards small external time-dependent forcings, when the noise intensity reaches some finite level. As such it highlights the possibility that noise, a universal phenomenon and yet one considered traditionally to constitute a nuisance, may actually play a constructive role in large classes of both natural and artificially designed systems. 

In the example you quote, the external time-dependent forcings are the steady vibrations of the table.
A: One possibility is the system having only a small set of initial conditions that lead to chaos - i.e., in this system the relative size of the chaotic attractor's basin of attraction is small.
That would mean that for most starting conditions the system won't display chaos: and a strong enough level of noise will be able to quickly move the system away from chaotic behavior back into regular motion.
