Change the forward O2 sensor. It's pretty easy. The sensor is available at any auto parts store, and should be about $70-80. The job will take about 15 minutes. Autozone will loan you the special socket for free.
Look behind the engine where all the exhaust pipes come together and you will see the sensor. Unplug, unscrew, put in the new one, plug it in and drive.
You may have to drive for a while before the code goes away, or you could clear the code with your OBDII tool if it is capable of doing that.
Iflylow - I hope you get this...It's been about a year I guess, and the P0135 error has come back and I can only run the car about 10 miles max after clearing the code before it comes back on...
So - I did what you said and replaced the Forward O2 Sensor which was right behind the engine. I drove around for a while after (about 15 miles) but the code didn't clear itself so I came home and cleared it myself and ran another 6-7 miles and it did not come back on.
Do you think I just didn't allow enough drive time for it to go away on its own, and if it comes back is there anything else it could be? Everything I've looked at says replace the sensor.