Current filamentation instability is observed and studied in a laboratory environment with a 60 MeV electron beam and a plasma capillary discharge. Multiple filaments are observed and imaged transversely at the plasma exit with optical transition radiation. By varying the plasma density the transition between single and multiple filaments is found to be k(p)σ(r)~2.2. Scaling of the transverse filament size with the plasma skin depth is predicted in theory and observed over a range of plasma densities. Lowering the bunch charge, and thus the bunch density, suppresses the instability.