Latin Phrase

They're both wrong.
Solo deo gloria

...hmm... I know why the discrepancy but I'm not sure which is right.

I blew it.
Upon further review, I find the the dative masculine singular of solus is not solo,
but soli.
So I'd say "Soli Deo gloria" is correct.

OK, I'll bite - why the discrepancy? Is it because it's not clear from the phrase what is the object? It would seem to me that "to God the glory" is the starting point, making God the object (which is why I'm confused by George's answer using the dative of solus). If God is the object, then "dei gloria" would be the base, and "solo" would be just modifying that phrase. Am I way off base?

It's not so much about grammar as it is about useage at various historical periods. Latin continued to be used in intellectual circles, particularly the Church, long, long after the fall of the Roman Empire. These people were extremely careful not to let the language "deteriorate" into something "vulgar" like Italian or Spanish or French. However, being human, as time wore on there was a slippage in the rules of grammar. This is easy to see if you compare some Medieval texts in Latin to "Classical" texts of the Romans. Solo may have seemed right to the Medieval scholars, but I agree with George -- soli is preferable if you're going the classical route.

Soli Deo Gloria
The Latin dative case is generally used to indicate the noun to whom
something is given. The phrase "to God" is the translation of the Latin "Deo",
the dative of "Deus". An adjective agrees in case with the noun it modifies,
so "soli" is also in the dative case.

The phrase is one of the five solas of the Protestant Reformation.

Thank you both for the detailed explanations. I continue to learn!

You're welcome, tjhudson.