The main trick here is the new Multiarch on Ubuntu Saucy and the need to enable it separately for Crouton.
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Install Crouton
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Install saucy
sudo sh -e ~/Downloads/crouton -t xfce -r saucy
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Start the chroot
sudo startxfce4
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Download and extract Android SDK starter
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Install Java 7
sudo apt-get install openjdk-7-jre
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Download platform tools
cd ~/android-sdk-linux/tools ./android
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Enable i386
sudo dpkg --add-architecture i386 sudo apt-get update
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Install ADB i386 dependencies
sudo apt-get install libc6:i386 libstdc++6:i386
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Run ADB
cd ~/android-sdk-linux/platform-tools ./adb