Any woodworkers (or others) how to cut this groove?

I need to cut, in a piece of 1/8” thick oak, a groove about 2” long by about 1/8” wide, along the grain direction

I have no power tools, but some rather nice chisels (including an 1/8” wide one). Any ideas on how to cut this cleanly? It could be a little wider than 1/8”, so I’m thinking maybe cut with the chisel and the smooth the edges out a little?