I found an example, how to show the LineNumbers from a RichTextBox in Windows Forms.
http://www.codeproject.com/Articles/38858/Line-Numbers-for-RichText-Control
ScintillaNET is a good component to try. It's the .NET version of Scintilla which is a key component in the Notepad++ editor (among others). I don't know how it compares to AvalonEdit, but I found it fairly easy to implement in my code and it has the feature you require (and many more).
Once you've installed the component and added it to your form, you can show line numbers by going to the properties of the control and setting Margins>Margin0>Width. You can also set this programmatically:
scintilla1.Margins.Margin0.Width = 20;
You might find the ScintillaNet documentation useful if you plan to take this route - I found it really helpful when I started.