although JPhi is right in what he says, he's also slightly wrong.
If you have taken a chunk out of your sidewall it's not necessarily dangerous in the slightest, it only becomes dangerous when you can see the cords because that is what can cause the tyre to bulge and blow out.
it is worth checking for any bulging after a 100 miles or so but if it's a part of the Tyre isn't raised up slightly then you will be fine.
The rubber on the Tyre isn't what keeps it structurally sound, It's the cords inside that provide the strength/structural integrity to handle 30+ psi, the rubber is just to keep the air in.
Worked in a Tyre/wheel garage for over 10 years and always had people coming in with small gauges where the cords weren't showing and they never had an issue waiting for the Tyre to wear down before replacing it.
Same question, lots of answers.
Notice the one response which suggests sealing the cut to stop water damage.
However, the outer tire rubber doesn't hold the air, the inner liner holds the air in. Thus a tire puncture means the inner liner gets a hole, and the inner liner must be properly patched.
A tire sidewall slice is quite common for 4x4 off roading trips, which I have done, and not a reason to replace the tire.
Here is a tire damage inspection chart. Some pretty serious problems that people drive around with.
Idiots! There is no reason for debate. If the tire has sidewall damage, replace the tire. Simple. A $200.00 tire is peanuts compared to the potential disaster a support failure will cause. I'm actually surprised that the issue is even up for question. Operating an automobile with less than adequate equipment is a threat to everyone else sharing the road. Stop thinking about yourself for a change and do the responsible thing, Go get a new one! The implication is negligence, also referred to as "half ass".