C.H. Morgan-Griffiths, the wealthy Carmarthen solicitor and diocesan registrar, by his own account first conceived the idea of building a Roman Catholic chapel in the vicinity of St Davids around 1928, about the time that work began on the construction of St Non's House. The original intention was to build at Whitewell Field, the site of one of the medieval chapels closely associated with the cathedral and the cult of St David, but as work advanced on the building of St Non's House as the Morgan-Griffiths' summer residence in 1929, it was decided to relocate the chapel on an adjacent site. Here it would overlook both the ruins of the medieval chapel, reputed birthplace of St David, and the site of St Non's Well. Morgan-Griffiths' wife was herself a Roman Catholic, and it was this fact which seems to have provided the initial impetus for the building of the Roman Catholic chapel at St Non's.

The publicity surrounding the construction of the chapel made much of the claim that St Non's was the first Roman Catholic place of worship opened at or near St Davids since the disruptions of the Reformation. Morgan-Griffiths made this claim himself, and it was echoed in the West Wales Guardian of 10 August 1934, in The Universe on the same date, and in The Tablet of the following day.