The most precise local measurements of H₀ rely on observations of Type Ia supernovae (SNe Ia) coupled with Cepheid distances to SN Ia host galaxies. Recent results have shown tension comparing H₀ to the value inferred from CMB observations assuming ΛCDM, making it important to check for potential systematic uncertainties in either approach. To date, precise local H₀ measurements have used SN Ia distances based on optical photometry, with corrections for light curve shape and colour. Here, we analyse SNe Ia as standard candles in the near-infrared (NIR), where luminosity variations in the supernovae and extinction by dust are both reduced relative to the optical. From a combined fit to 9 nearby calibrator SNe with host Cepheid distances from Riess et al. (2016) and 27 SNe in the Hubble flow, we estimate the absolute peak J magnitude M_J = −18.524 ± 0.041 mag and H₀ = 72.8 ± 1.6 (statistical) ±2.7 (systematic) km s^-1 Mpc^-1. The 2.2% statistical uncertainty demonstrates that the NIR provides a compelling avenue to measuring SN Ia distances, and for our sample the intrinsic (unmodeled) peak J magnitude scatter is just ~0.10 mag, even without light curve shape or colour corrections. Our results do not vary significantly with different sample selection criteria, though photometric calibration in the NIR may be a dominant systematic uncertainty. Our findings suggest that tension in the competing H₀ distance ladders is likely not a result of supernova systematics that could be expected to vary between optical and NIR wavelengths, like dust extinction. We anticipate further improvements in H₀ with a larger calibrator sample of SNe Ia with Cepheid distances, more Hubble flow SNe Ia with NIR light curves, and better use of the full NIR photometric data set beyond simply the peak J-band magnitude.