Why does your Chevy Tahoe make a screeching noise when you turn the steering wheel to the left?

Have you checked your wheel hub and bearing for excessive wear? Another possibility is that your Power Steering system (if your truck has it) could be either low on fluid or failing.

To completely and accurately answer this question I'll need more information:

1. Where in general is the screeching noise coming from?
2. Is the noise accompanied by a thumping, grinding, or vibration?
3. Does this noise happen EVERY time you make a left turn? If not, at what speed(s) in general does the screeching occur?
4. Is there an odd burnt smell that accompanies the noise?
5. Have you noticed any recent oily deposits under your truck where you normally park or after it has sat for a while?

Upon reflection, a third possibility comes to mind. Check the swaybar link and the bushings for the driver's front wheel. You might be in the beginning stages of link failure. While the link itself does not move or rotate, it does have an effect on how the wheel behaves. I had a similar problem with my Jeep and it drove me nuts figuring out what was wrong. It turned out that BOTH of my swaybar links were shot. Mechanics call it the "Death Wobble" because it is a serious suspension issue, though it is easily fixed. Fortunately I was able to replace them myself with link replacement kits available at my local auto parts shop for about $150. The kits came complete with the links, bushings, and all new fasteners so I didnt have to re-use any "questionable" nuts and bolts.