You can now do this without the use of Android SDK.
In the latest version of chrome (I am working on 34.0.x):
- Navigate to
chrome://inspect/ - Check
Discover USB Devices - Plug in your phone via USB. A popup should spawn asking for permission to connect to your computer. Accept it.
There will now be an item on the chrome://inspect/ pages for your phone, and you can click inspect. Dev tools will spawn and voila!