Some chaotic systems are deterministic, others are not. For instance, flipping a coin is chaotic, but quite deterministic - you give the same coin the same impulse and it behaves in the same way.
I doubt flow is a deterministic chaotic system. The same situation will produce different results, even though they may be very similar on a large scale. For instance, a wing at a given angle of attack at a given speed, temp etc will produce the same amount of lift, but from a computational point of view there will be differences. For instance the picture of separated flow will be different and unpredictable between two exposures taken a small time apart. This is not true for the coin.
If you could model every particle in the fluid, with a large number of paramaters such as temperature, speed, mass etc then you could possibly come up with a good approximation, however the amount of points and variables is so huge that even a big array of very fast computers is going to take a very long time with even the simplest problem.
Notwithstanding that, the micro and macro worlds are very different and flow is not usually considered to be a bunch of particles. CFD uses elements, but these are many many times the size of the particles that make up the flow, and are subject the different laws - for instance the electromagnetic force is important in molecules, but not usually in flow.