sql - Creating join based on multiple fields using ArcGIS Desktop?

I have two feature classes in a File Geodatabase that I would like to join based on multiple fields. I've searched this site and Google and all I have come up with was to use the Make Query Table tool. I've tried this, but I keep getting an SQL error. My SQL is pretty poor and I'm pretty sure I'm missing something.

I am aware I can create a new field and concatenate the values from my fields, but I would like to avoid this, if possible.

I'm using something that looks like this:

(Table1.Field1 = Table2.Field1) AND (Table1.Field2 = Table2.Field2) AND (Table1.Field3 = Table2.Field3)

When I verify the query, I get an error that says:

There was an error with the expression. 
An Invalid SQL statement was used.

An invalid SQL statement was used. [Table1]

Also, if someone has another solution that doesn't use this tool, I'm happy to hear about it.