The microphysical properties, such as effective viscosity and conductivity, of the weakly magnetized intergalactic plasma are not yet well known. We investigate the constraints that can be placed by an azimuthally resolved study of the cold front in Abell 3667 using similar to 500 ks archival Chandra data. We find that the radius of the interface fluctuates with position angle and the morphology of the interface is strikingly similar to recent numerical simulations of inviscid gas-stripping. We find multiple edges in the surface brightness profiles across the cold front as well as azimuthal variations, which are consistent with the presence of Kelvin-Helmholtz instabilities (KHIs) developing along the cold front. They indicate that the characteristic length-scale of KHI rolls is around 20-80 kpc. This is the first observational indication of developing KHIs along a merger cold front in a galaxy cluster. Based on the KHI scenario, we estimated the upper limit of the intracluster medium effective viscosity. The estimated value of mu less than or similar to 200 g cm(-1) s(-1) is at most 5 per cent of the isotropic Spitzer-like viscosity. The observed apparent mixing towards the outer edges away from the tip of the front provides an additional evidence for suppressed viscosity.