That depends; it could be either redundant or contradictory. If I understand it correctly, "stochastic" only means that it's governed by a probability distribution but not which kind and there are lots of different kinds: https://en.wikipedia.org/wiki/List_of_probability_distributi... . It's redundant for a continuous uniform distribution where all outcomes are equally probable but for other distributions with varying levels of predictability, "stochastic chaos" gets more and more contradictory.
Stochastic means that its a system whose probabilities don't evolve with multiple interactions/events. Mathematically, all chaotic systems are stochastic (I think) but not vise versa. Or another way to say it is that in a stochastic system, all events are probabilistically independent.
Yes, its a hard to define word. I spent 15 minutes trying to define it to someone (who had a poor understanding of statistics) at a conference once. Worst use of my time ever.