(Note: my HDD crashed recently and until I get that fixed I can't really make LDraw images. I did create one for this beforehand, but it's on the same HDD.)
As jfyelle said the solution consists of using one LEGO element which has an odd ldu dimension somewhere. There is such an element, which isn't even new or particularly rare, that is, the Fence 1 x 4 x 2:
The centre part has a thickness of 6 ldu, which means that there are 7 ldu on each side. So if you add a 2x4 plate in it, the thickness of the plate (8 ldu) means that it will stick out by exactly one ldu. If your fence is one red brick, just put a 1x4 brick and a 1x4 brick with for knobs on the other to connect to the plate. Your two red bricks should then be 1 ldu apart.
I did learn that trick from Didier Enjary in his excellent Advanced Building
Techniques Guide which is well worth reading. That document contains a whole chapter on offsetting, but curiously the 1 ldu offset isn't listed explicitly; rather, the fence element and its 7 ldu offset is mentioned casually in the SNOT section.