I solved this issue by setting buildToolsVersion in my build.gradle file to match the latest version of the Android SDK Build-tools in the SDK manager.

In my case, I have the Android SDK Build-tools version 22.0.1 installed, so I set buildToolsVersion accordingly:
apply plugin: 'com.android.application'
android {
compileSdkVersion 22
buildToolsVersion "22.0.1"
...
After making that change, my app builds uneventfully.