C#, is there such a thing as a "thread-safe" stream?

I am redirecting the output of a process into a streamreader which I read later. My problem is I am using multiple threads which SHOULD have separate instances of this stream. When I go to read this stream in, the threading fudges and starts executing oddly.

Is there such a thing as making a thread-safe stream?
EDIT: I put locks on the ReadToEnd on the streamreader, and the line where I did: reader = proc.StandardOutput;