Chaotic systems are predictable: The relevant quantities are probability distributions.
Evolution, also, involves dealing with probability distributions, that are, also, predictable.
Whether evolution describes deterministic chaos is, however, an inependent question. Not all systems, that are described by probability distributions, are deterministic chaotic systems.
Next step evolution, that prediction, is logically a many-body problem. Therefore, it is not precisely predictable. Probable guesses can be put forth. -g
When Charles Darwin tried to explain how natural selection could act in a way that we might call progressive, he realized that his theory needed something more than simple adaptation. He said that progressive evolution came from the interactions between life forms, such as when cheetahs becoming faster made them more likely to catch impalas.
He contrasted this with adaptation that can happen when an organism responds to abiotic changes in the environment, such as a change in temperature or rainfall, etc.
If we break cases down into these two categories, we can say that cases of adaptation are fairly predictable, while progressive evolutionary cases are not at all predictable.
A good example of adaptation is the case of the Peppered Moth, which was first noticed to change from its normally white color to an almost black color at the same time when coal burning became a popular source of heat, in the 1800s. Later, when other sources of heat replaced coal burning, the moths changed back to their original color.
The reason for the change is quite clear, because if there is soot on the trees, a white moth will stand out and be easy pickings.
I think it is safe to say that if coal burning once again became popular in that region and soot began covering trees, we can safely predict that the Peppered Moths will once again change to a darker color. This is a clear case of adaptation to abiotic changes in the environment.
It, of course, will not be exactly predictable because the birds that feed on the moths may be affected by other factors. This is not an abiotic effect however. So, the predictable part is only the adaptation to abiotic changes alone.