I am developing an android application as part of a project, and am using Google places API to display places of interest based on location. I am using the PlacePicker Inent
Add compile 'com.google.android.gms:play-services-location:8.1.0'
in gradle
Have you double checked that your API key is associated with your application (package name and SHA-1 fingerprint of your app's certificate) in the Developer Console?
You can find instructions at Signup and API Keys. Make sure to set it up for both your debug and your release certificates.
I hope that helps!