VIM: Show 3 characters on the left side of the window

Context

I am using the NERDTree plugin.

The only thing that annoys me is the visual vertical border between NERDTree itself and my code. I am a little annoyed to read my code. My current setup looks something like this:

........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________
........................#________________________________________________

where ... = NERDTree, _ = my actual code and ### = some vertical gray border.

Now I want something like this:

........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________
........................#   ________________________________________________

The idea is that I somehow insert a 3-digit border between the NERDTre vertical divider and to the left of my actual code.

Now I can almost achieve this with "set nu" - except that instead of spaces I get a bunch of numbers. I would like something like "set nub", except instead of line numbers, I just get spaces.

Question:

How to achieve the above?