James Chastek has a brief post on Two meanings of "chance" that is very brief, but has revealing comments, including this one:
There is a very long history of denying the reality of chance, and there is some force to it- the sciences not infrequently find causes for things thought to be by chance, like the generation of gnats, or hand washing and patient health.
Here is the important distinction between luck and chance. It wasn’t important here, but it is important in itself. Luck (good and bad) results from some ignorance or deficiency in the power of the agent, chance in nature proceeds from some deficiency in interior causes, primarily from matter.
Aristotle called chance a real cause, but cause per accidens. It is not a proper cause, but it is that which is responsible for something, and so satisfies some notion of cause. This is a tricky question, one that De Koninck dedicated much of his career to.
The modern educated common wisdom basically accepts the billiard-ball model of physics, and tends to assume a mechanistic view of nature built upon this model. However, the trouble is that material things are not really perfect enough to be deterministic. There is an order of being argument lurking in the background here, that only a perfect cause could make something happen the same way every time, whereas every material thing is less than perfect, and therefore cannot be a part of a deterministic chain of causation. It is, however, close enough to make it work most of the time.
I suspect that some of the resistance to this idea is that chance is a kind of negation, as Chastek says in an earlier post, "a supposedly pure world of complete unintelligibility". Chance or possibilty seen as a lack of knowledge thus undermines our ability to know the world, because it would seem that as pure unintelligibility, chance events would mean that anything could happen. Thus, I think there is a fear that denying the deterministic account means denying the power of modern science.
However, in an Aristotelian account, chance can serve a purpose in nature. It is not really that anything could happen, but rather things tend toward certain ends, even if they don't quite make it all the time. Thus you end up with distributions of measurements when you study natural things in the modern mathematical way. Sometimes there can be a "true" number towards which the natural thing is tending, and the tightness of the distribution is related to the power of the cause. The actual power of modern science is to be able to say, the probability the value found is between this number and that, is X%.
I think chance could perhaps be posited as one of the things that allows sufficient uniformity in nature for us to be able to predict things for the most part. It seems that if everything were in fact completely deterministic, every event would be unique, and in a sense, unpredictable for us, because one of our primary ways of knowing is inductive, working from particular events to what happens for the most part. Thus a universe with some looseness to its physical causes is actually more intelligible to us rather than less.