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As far as I know, there is no Chi Velorum. SIMBAD has no listing of it. Generally, if there is a Bayer designation it would be used.
The original Bayer designations (alpha to omega) were given to Argo Navis which was later split into Carina, Puppis and Vela. There was a Chi Puppis but that designation is now given to Chi Carinae.
None of the three constellations have complete Bayer designations for this reason. Most kept their original Greek designation with the constellation name now depending on what border they lie within. So each have about ⅓ of the Greek letters without overlap.
For example:
Alpha Carinae. There is no Alpha Puppis or Alpha Velorum.
Gamma Velorum. There is no Gamma Carinae or Gamma Puppis.
Zeta Puppis. There is no Zeta Carinae or Zeta Velorum.
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