Without getting into a long tangent about what is genuinely random, let’s agree that St Thomas Aquinas believed that nothing in the world happens by chance. St Thomas Aquinas was not a scientist and had no access to theories of quantum mechanics but relied, instead, on his own belief about God’s nature.
When St Thomas says that nothing in the world happens by chance, he means just that, namely, in the eyes of God and of divine providence, nothing happens by chance nor is it possible. This can be argued from many angles such as in philosophy and metaphysics, Holy Scripture, the teaching of the Church such as what is said concerning divine providence in the CCC beginning with #302. It appears to me that chance excludes belief in divine providence. God’s intellect and will is the cause of things, indeed He is the first cause of whatever takes place in the world, and He knows whatever and all the effects that result from His causality and wills to happen. God created the world from a plan he conceived in his intellect for it and for an end and purpose in which are included the entire history of the universe and all the effects which result from his universal causality. God’s will does not operate blindly but according to the plan and knowledge of his intellect.
No, St Thomas was not a scientist. He was a philosopher, metaphysician, and principally a theologian. As a philosopher and metaphysician, St Thomas argues from metaphysical principles which are meant to be the most universal kind of natural knowledge above that of the natural sciences such as physics. The theories of modern quantum mechanics which you are appearing to present as an argument for the role of chance or pure randomness in the world does not do away with St Thomas’ teaching. The fact is we only know so much about the world from the study of nature and quantum mechanics and we will probably never know everything about how the world operates. It sure is a marvel of the creative activity of God.
Holy Scripture says “she [Wisdom] reaches from one end of the earth to the other, and ordering all things well” (Wisdom 8:1). And “Thou hast ordered all things in measure, number, and weight” (Wisdom 11:21). Everything in the world is ordered and governed by the providence of God who is the absolute Lord over history and the world (cf. CCC#304). This does not mean that secondary causes are not real causes, they are real causes of things, but their causality is dependent on the first cause.
I think, though, that you and he are relying on a narrow understanding of causality. Suppose I throw a die. Whatever number comes up, I was the cause of it.