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We present year-long, near-infrared Hubble Space Telescope WFC3 observationsused to search for Mira variables in NGC 1559, the host galaxy of the Type Iasupernova (SN Ia) 2005df. This is the first dedicated search for Miras,highly-evolved low-mass stars, in a SN Ia host and subsequently the firstcalibration of the SN Ia luminosity using Miras in a role historically playedby Cepheids. We identify a sample of 115 O-rich Miras with P < 400 days basedon their light curve properties. We find that the scatter in the MiraPeriod-Luminosity Relation (PLR) is comparable to Cepheid PLRs seen in SN Iasupernova host galaxies. Using a sample of O-rich Miras discovered in NGC 4258with HST F160W and its maser distance, we measure a distance modulus for NGC1559 of mu1559 = 31.41 +/- 0.050 (statistical) +/- 0.060 (systematic) mag.Based on the light curve of the normal, well-observed, low-reddening SN 2005df,we obtain a measurement of the fiducial SN Ia absolute magnitude of MB0 =-19.27 +/- 0.13 mag. With the Hubble diagram of SNe Ia we find H0 = 72.7 +/-4.6 kms-1 Mpc-1. Combining the calibration from the NGC 4258 megamaser and theLarge Magellanic Cloud detached eclipsing binaries gives a best value of H0 =73.3 +/- 4.0 km s-1 Mpc-1. This result is within 1-sigma of the Hubble constantderived using Cepheids and multiple calibrating SNe Ia. This is the first offour expected calibrations of the SN Ia luminosity from Miras which shouldreduce the error in H0 via Miras to ~3%. In light of the present Hubble tensionand JWST, Miras have utility in the extragalactic distance scale to checkCepheid distances or calibrate nearby SNe in early-type host galaxies thatwould be unlikely targets for Cepheid searches.

Hubble Space Telescope Observations of Mira Variables in the Type Ia Supernova Host NGC 1559: An Alternative Candle to Measure the Hubble Constant