In the Metaphysics Aristotle makes the case for chance and uncaused causes (causa sui) and in the Nicomachean Ethics he shows our actions can be voluntary and "up to us" so that we can be morally responsible.

Nor is there any definite cause for an accident, but only chance (τυχόν), namely an indefinite (ἀόριστον) cause.
(Metaphysics, Book V, 1025a25)¹

It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will this be, or not? Yes, if this happens; otherwise not.
(Metaphysics, Book VI, 1027a29) ²

Aristotle rejected determinism in his statement on chance. Unfortunately, his description of chance as "obscure" (ἄδηλος) to human reason led centuries of philosophers to deny the existence of chance:

Causes from which chance results might happen are indeterminate; hence chance is obscure to human calculation and is a cause by accident.
(Metaphysics, Book XI, 1065a33) ³

His definition of the voluntary will as caused from within an agent (the first agent-causal libertarianism) is still valid today.

If then whereas we wish for our end, the means to our end are matters of deliberation and choice, it follows that actions dealing with these means are done by choice, and are voluntary. But the activities in which the virtues are exercised deal with means. Therefore vίrtue also depends on ourselves. And so also does vice. For where we are free to act we are also free to refrain from acting, and where we are able to say No we are also able to say Yes; if therefore we are responsible for doing a thing when to do it is right, we are also responsible for not doing it when not tο dο it is wrong, and if we are responsible fοr rightly not doing a thing, we are also responsible fοr wrongly doing it. But if it is in our power tο dο and tο refrain from doing right and wrong, and if, as we saw, being good οr bad is doing right οr wrong, it consequently depends οn us whether we are virtuous οr vicious.

But if it is manifest that a man is the author of his own actions, if we are unable to trace conduct back to any other origins than those within ourselves, then actions of which the origins are within us (ἐν ἡμῖν), themselves depend upon us (ἐφ' ἡμῖν), and are voluntary (ἐκούσια - willed).
(Nichomachean Ethics, III.v.6, 1113b19-22) ⁴

Even when our character adequately determines our choices, since we were directly responsible for forming at least part of that character at an earlier time in our lives, so we are now indirectly responsible for all those choices.

But suppose somebody says: "All men seek what seems tο them good, but they are not responsible for its seeming gοod: each man's conception οf his end is determined by his character."
(Nichomachean Ethics, III.v.17, 1114a30-1114b1 ) ⁵

If then, as is said, our virtues are voluntary (and in fact we are in a sense ourselves partly the cause of our states of character, and it is our having a certain character that makes us set up an end of a certain kind), it follows that our vices are voluntary also; they are voluntary in the same manner as our virtues.
(Nichomachean Ethics, III.v.20, 1114b22-25 ) ⁵

That Aristotle believes in an open and ambiguous future with alternative possibilities is also shown by his denial of the Master Argument for determinism of Diodorus Cronus, in the form of Aristotle's famous "sea battle."

Diodorus argued from an assumed necessity of past truths (which is understandable, if a misapplication of logic to physical reality) that something is impossible that neither is or ever will be true.

Aristotle reframed the argument as the truth or falsity of the statement that a sea battle will occur tomorrow. Despite the law of the excluded middle, which allows no third case, Aristotle concluded that the statement is neither true nor false, supporting an ambiguous future.

What is, necessarily is, when it is; and what is not, necessarily is not, when it is not. But not everything that is, necessarily is; and not everything that is not, necessarily is not. For to say that everything that is, is of necessity, when it is, is not the same as saying unconditionally that it is of necessity. Similarly with what is not. And the same account holds for contradictories: everything necessarily is or is not, and will be or will not be; but one cannot divide and say that one or the other is necessary.

I mean, for example: it is necessary for there to be or not to be a sea-battle tomorrow; but it is not necessary for a sea-battle to take place tomorrow, nor for one not to take place — though it is necessary for one to take place or not to take place. So, since statements are true according to how the actual things are, it is clear that wherever these are such as to allow of contraries as chance has it, the same necessarily holds for the contradictories also. This happens with things that are not always so or are not always not so. With these it is necessary for one or the other of the contradictories to be true or false — not, however, this one or that one, but as chance has it; or for one to be true rather than the other, yet not already true or false.
(De Interpretatione, IX, 19a23-39 ) ⁶

Aristotle never denied the law of the excluded middle, merely that the truth or falsity of statements about future events does not exist yet. Note that this implies at least some things in the past may be changed in the future, i.e., the truth values of statements about the future.

In the century following Aristotle, Epicurus proposed a random swerving of some atoms, at no particular places and times, as the cosmological source of chance. Although this physical model for chance is ingenious and anticipated twentieth-century quantum mechanics, Epicurus provides little of deep significance for free will and moral responsibility that is not already implicit in Aristotle.