Commercially useful, bulk superconductors typically require stabilization using a normal metal cladding for reasons of electrical, thermal, and mechanical protection and, in general, need to be drawn into fine fibers and wound into a magnet configuration. The recent discovery of high‐TC superconductor materials such as Ba2YCu3O7 stimulated worldwide interest in the subject, however, with much concern about fabricability of such brittle ceramic materials into desirable fine wire geometry. In this letter, we report preliminary success in the fabrication of fine‐wire, composite superconductors consisting of a high‐conductivity normal metal shell such as Ag or Cu/Ni/Au and a superconducting core of Ba2YCu3O7 oxide. The wire is would into a coil, and then heat treated to produce the desired chemistry in a dense structure. The resistivity of the composite wire is measured to be zero at ≊90 K (in zero field) with a zero‐field critical density of ≊175 A/cm2. Microscopy and x‐ray analysis show that the superconducting core is continuous, and retains phase composition after wire drawing and heat treatment. These results demonstrate the feasibility of producing superconducting ceramic composite wire, although the practical applications must await the resolution of many practical problems and reliability issues.