Unfortunately, you cannot fork in C# like you can in C on POSIX-compatible operating systems.
You have a few options. Since you’re just looking to protect against infinite loops, you could just spawn a new Thread (a new one, not a ThreadPool one or a Task one). Then, you can call Abort on the thread if you need to kill it. This will trigger a ThreadAbortException in the other thread.
Your other option is an AppDomain. You can create a new AppDomain using the currently running assembly relatively trivially. Then, you make a call into a proxy object that actually exists across the domain. The proxy will use old-school .NET remoting to call the method on the real object (so no generic-passing, etc., since you’re limited by .NET 1.1-based constructs).
Be aware that none of the above strategies will protect you from a crash in unmanaged code. Since AppDomains are a managed construct, you cannot use them to abort unmanaged hang-ups.
If you’re really, really, really determined to get a second OS-level process, you can also generate a new executable assembly in a temporary file on the fly and start that in a new process. See here for an MSDN article on new assembly generation. Be aware that this is not trivial at all.