A well-established "coextrusion" technique is applied to visualize and document a newly found self-oscillation due to an unstable boundary condition in capillary flow of high-density polyethylene. In contrast to the other types of self-oscillations of interfacial origin reported in the literature, the phenomenon can only occur in a die where the upstream portion of the capillary die wall has a surface condition different from that of the downstream portion. The self-oscillation phenomenon takes place under a constant pressure when one half of the die wall (coated with a layer of fluoropolymer) assumes steady slip due to adhesive breakdown, and the boundary condition of the other half switches between no-slip and slip states through the cohesive chain disentanglement mechanism.