You missed the whole point. Randomness exists in both normal and chaotic systems. The difference is that in normally distributed systems, randomness can be predicted.
A major recent criticism is of some economic models which have assumptions to the effect of "returns on this investment will be normally distributed." The criticism is that evidence seems to suggest that returns are not actually normally distributed; rather they have "fat tails," meaning that extreme events are more likely than with a normal distribution. And this error causes economic models to discount the role of these unlikely extreme events.
The Black-Scholes model effectively models stock prices as Brownian motion. This boils down to a single assumption: stock prices are the buildup of lots of very small INDEPENDENT random events (with FINITE variance) that occur over short times periods; this leads straight to Brownian motion. Brownian motion is indeed continuous; however, it is nowhere differentiable with probability 1. Because of the assumptions of finite variance and independence, the CLT tells us that returns will be normally distributed. So here, people pretty much agree that it's always these assumptions of independence that cause these models to predict poorly.
This is totally different from chaos theory. First of all, chaotic systems are not necessarily complex. Here's a chaotic map with a "nice little formula":
f : [0,1) -> [0,1)
f(x) = 2*x (mod 1)
If the stock market movements were normally distributed, crashes would be extremely rare. Something like 1 every 10,000 years. Virtually all economic models assume something to be true that we know isn't.
However, we can't predict the weather, nor can we predict the earthquakes. And as you correctly point out, the reason for this is chaos. The reason is not that we don't understand the underlying processes that govern these dynamics. Rather, the uncertainties in our initial conditions increase exponentially with time (due to chaos) and make long-term predictions unreliable.
The fact that it is easy because the distribution is normal has nothing to do with the randomness. Really.
You cannot 'predict' randomness in a normal distribution as you cannot in a geometric or uniform.
In chaos theory, the best you can hope for is strange attractors. Unfortunately, economics doesn't even seem to have these.