Chrysippus' god-argument is not, strictly speaking, a proof of the existence of a god. It is rather an appeal to what he thinks is common sense, and to the consequences of not believing.
The first part, the appeal to common sense, goes something like this:
1) If there is anything in nature that we can't have made then something greater than us made it;
2) That something is what we call a god.Of course, he is assuming that everything that exists must exist because it was made, and that it was made designedly by a single cause. We could object that natural arrangements might have more than one lesser natural cause; or we could contest the whole notion of greater and lesser and dismiss this part of his argument fairly easily.
The second part makes a case that at least invites us to be cautious about dismissing it too readily. It goes like this:
3) Unless there is divine power, human reason is the greatest thing we know of and can possess;
4) So if there are no gods, then we are the greatest beings in the cosmos. In which case, we are the gods.Of course there might be other things we don't know of that are more powerful than we are; or we might (wisely) regard nature as more powerful than we are.
But the most helpful part, I think, is (4), which stands as an invitation to consider who we are as we face the cosmos. We think of ourselves as natural, but we also think of ourselves as standing somehow apart from nature.
So it may be that there is nothing in the cosmos wiser or more clever than we are. We should be honest about this and acknowledge the real possibility that this is the case.
But Chrysippus invites us also to consider the consequences of that belief, since it could be taken as license to act as we will. The danger, as he sees it, is that we might become the sort of people who worship ourselves. This is dangerous in part because it impedes growth; we become like what we worship, and if we worship only ourselves, then we become our own best ideal. I will speak for myself when I say that I, at least, am a cramped and stingy ideal.
Many of the Stoics are content to name nature as god; what matters is that there always be something worth our attention and admiration. I'm reminded of the wise words of David Foster Wallace, who said that
There is no such thing as not worshipping. Everybody worships. The only choice we get is what to worship. And an outstanding reason for choosing some sort of god or spiritual-type thing to worship - be it JC or Allah, be it Yahweh or the Wiccan mother-goddess or the Four Noble Truths or some infrangible set of ethical principles - is that pretty much anything else you worship will eat you alive.You can read the rest of his brief, insightful talk here (or by searching for "This Is Water.")
Wallace comes pretty close to Chrysippus. Neither is trying to convert you to a religion, neither is trying to set the rules for your life, but both are reporting on what they have seen when they have ventured in the direction of denying all the gods: off in that direction, they found they could escape all the gods except the god they then found that they forced themselves to become.
Which, to paraphrase Wallace, is a good reason for choosing to posit some god which, if it existed, would be worth your worship. And then, maybe, to test it by trying to worship it as though it were really there.