Android AddThis sdk + Facebook sdk won't build in Android Studio

Android AddThis sdk + Facebook sdk won't build in Android Studio

I have a project I'm working on in Android Studio that currently uses the
Facebook SDK for retrieving some information about a Facebook user. It
works pretty well.
I also need to implement AddThis, however when I try to compile this
project with both SDKs referenced, I get the error:
Android Dex: [<removed>] com.android.dx.util.DexException: Multiple dex
files define Lcom/facebook/android/AsyncFacebookRunner$1;
Inside the AddThis .jar, as expected,
com.facebook.android.AsyncFacebookRunner exists. Obviously it also exists
in the Facebook SDK module. There is functionality that I need in both
modules which only exists in one. I can't just go into the AddThis jar and
delete all of the Facebook code.
Does anyone know a way to handle this type of situation?