We present high angular resolution observations of HC$_3$N J=5--4 line and 7 mm continumm emission from the extreme carbon star CIT 6. We find that the 7 mm continuum emission is unresolved and has a flux consistent with black-body thermal radiation from the central star. The HC$_3$N J=5--4 line emission originates from an asymmetric and clumpy expanding envelope comprising two separate shells of HC$_3$N J=5--4 emission: (i) a faint outer shell that is nearly spherical which has a radius of 8arcsec; and (ii) a thick and incomplete inner shell that resembles a one-arm spiral starting at or close to the central star and extending out to a radius of about 5arcsec. Our observations therefore suggest that the mass loss from CIT 6 is strongly modulated with time and highly anisotropic. Furthermore, a comparison between the data and our excitation modelling results suggests an unusually high abundance of HC$_3$N in its envelope. We discuss the possibility that the envelope might be shaped by the presence of a previously suggested possible binary companion. The abundance of HC$_3$N may be enhanced in spiral shocks produced by the interaction between the circumstellar envelope of CIT 6 and its companion star.