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With Mathematica 11.2 I could import this FITS file without problems in about 20-30 seconds using:

Import["filename.fits.gz", "TableData"]

With Mathematica 11.3 it failed after trying for 300 seconds.

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  • $\begingroup$ I can't test it because I don't have 11.3, but I can confirm that it works on 11.2; this looks like a problem you should report to Wolfram Support. $\endgroup$ – MarcoB Jun 29 '18 at 15:03
  • $\begingroup$ It seems you can workaround it by Import["filename.fits.gz", "Table"] $\endgroup$ – SuTron Jul 4 '18 at 7:32

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