If you intend to allow users/administrators to change the string, I agree with the other answers, and I'd suggest putting it in settings.
If you don't want it to be editable after deployment and it will only be modified by you and your developers, then I would put it in an embedded resource (note, this is not the same as a .resx file). You would read it at runtime like this:
Assembly assembly = Assembly.GetExecutingAssembly();
Stream stream = assembly.GetManifestResourceStream(“MyAssemblyNamespace.MyTextFile.txt”);
StreamReader reader = new StreamReader(stream);
string theText = streamReader.ReadToEnd();
Update: This is solution that is easy to maintain. The .txt file will just be another file in your solution explorer in Visual Studio and you can edit it just like any other file, keep it under source control like any other file, etc. To turn it into an embedded resource by changing the Build Action in the properties window to "Embedded Resource".
The end result is that your file(s) get embedded in your DLL so that you only have 1 DLL to distribute instead of a DLL and a folder of files that have to move around together.
Update 2: Regarding "production debugging", this is a very static solution, and so you won't be able to change the contents of the text file at runtime because the file is baked into the DLL at compile time. For reading the contents of the file, you can use tools like reflector to view the embedded resources of a DLL. You could also write a simple command line tool that dumps all the embedded .txt files from a DLL into individual files for you to look at.
For memory usage, there isn't a solution more efficient than "I load it from a file into memory only exactly when it is needed". You have to decide whether the improved maintainability and deployment is worth the cost of a little extra memory when your DLL is loaded into memory for your specific situation. That said, you haven't said how large these files are. If they are really huge (megabytes+), I would probably not use this solution and would go with loose files on the hard drive. If they are generally pretty small (hundreds of kilobytes), I wouldn't worry about the extra memory unless you are in some kind of embedded device situation where RAM is really tight.