Abstract We report on Chandra X-ray observations of SN 2016jae and SN 2018cqj, both low luminosity Type Ia supernova that showed the presence of a H line in their early optical spectrum. No X-ray emission is detected at the location of either SN. Upper limits to the luminosity of up to 2 × 1040 erg s−1 are calculated for each SN, depending on the assumed spectral model, temperature and column density. This luminosity is comparable to that of another low-luminosity Type Ia SN, SN 2018fhw, that was observed with Chandra. It is generally lower than upper limits calculated for Type Ia-CSM SNe observed in X-rays, and also below that of SN 2012ca, the only Type Ia-CSM SN to have been detected in X-rays. Comparisons are made to other Type Ia SN with a H line observed in X-rays. The observations suggest that while the density into which the SN is expanding may have been high at the time the Hα line was detected, it had decreased considerably by the time of X-ray observations.