This paper reports experimental results and modeling relating to the ambient temperature, cold extrusion of chocolate. In particular, extrusion conditions are given where two different modes of instability are described and modeled. In the first case, at low flow rates, a stick-spurt instability is observed, which leads to large amplitude fluctuations in the extrusion pressure and extrudate velocity. This instability is modeled as a modified relaxation oscillation process in which the combined nonlinear plastic flow behavior of the chocolate and the compressibility of the material in the reservoir control the instability mechanism. The second mode of instability, observed for a specific thermal history, concerns the unusual extrusion of a "necklace" structure consisting of beads regularly spaced on a narrow extrudate core. This instability is explained in terms of the steady core-annular coextrusion of two Bingham-plastic chocolate components having different yield Stresses.