Android class “already added” when building

I am working on an Android project constructed of:

• The main app (very lightweight wrapper + AndroidManifest.xml)
• The main library (where all the real work gets done)
• Facebook-android-sdk
• HockeySDK-Android

Recently, I started seeing the following error when building the app using ant:

[dx] UNEXPECTED TOP-LEVEL EXCEPTION:

[dx] java.lang.IllegalArgumentException: already added: Lcom/facebook/android/R$anim;

[dx] at com.android.dx.dex.file.ClassDefsSection.add(ClassDefsSection.java:123)

[dx] at com.android.dx.dex.file.DexFile.add(DexFile.java:163)

[dx] at com.android.dx.command.dexer.Main.processClass(Main.java:486)

[dx] at com.android.dx.command.dexer.Main.processFileBytes(Main.java:455)

[dx] at com.android.dx.command.dexer.Main.access$400(Main.java:67)

[dx] at com.android.dx.command.dexer.Main$1.processFileBytes(Main.java:394)

[dx] at com.android.dx.cf.direct.ClassPathOpener.processArchive(ClassPathOpener.java:245)

[dx] at com.android.dx.cf.direct.ClassPathOpener.processOne(ClassPathOpener.java:131)

[dx] at com.android.dx.cf.direct.ClassPathOpener.process(ClassPathOpener.java:109)

[dx] at com.android.dx.command.dexer.Main.processOne(Main.java:418)

[dx] at com.android.dx.command.dexer.Main.processAllFiles(Main.java:329)

[dx] at com.android.dx.command.dexer.Main.run(Main.java:206)

[dx] at com.android.dx.command.dexer.Main.main(Main.java:174)

[dx] at com.android.dx.command.Main.main(Main.java:95)

[dx] 1 error; aborting