St. Anselm is usually known for his ontological argument, but he also supported various other arguments for God's existence. One of these is a version of the cosmological argument, which seeks to establish that, "there is . . . some one being which is supremely good, and supremely great, that is, the highest of all existing beings." 
1. Something good exists.
The axiological realist will grant this premise. However, it will not be accepted by moral nihilists. The audience of this proof, then, will be restricted to those who acknowledge that there really are, objectively-speaking, good things.
2. That which is good is either good through itself or through another.
Premise (2) will be accepted by those who adhere to even a minimal Principle of Sufficient Reason. Only if some attribute of a thing is inexplicable would (2) be false, or possibly false.
3. Different things are good by virtue of a single principle.
Anselm anticipates an objection, here. A horse is said to be good because he is both strong and swift. Yet, a robber can also be strong and swift, but surely the robber is not good. It's at this point that Anselm appeals to teleology: the horse's strength and swiftness is good due to its usefulness, whereas the robber's strength and swiftness is bad because his actions are harmful. It is the end, goal or purpose, then, that Anselm appeals to.
Further, two things are said to be just because they both participate in the single quality of justness. Likewise, then, two (or more) things are said to be good because they participate in the single quality of goodness. Now, this quality of goodness is itself a great good, Anselm says. Therefore, there is a single principle of goodness, the Supreme Being (God), which is the cause of all goodness in good things.
4. Therefore, a single principle of goodness exists.
 St. Anselm, "Monologium," Ch. 1, from Basic Writings, translated by S.N. Deane, Open Court Publishing Company, 1962, p. 86.