The graveyard just north-west of Kildare's Market Square holds considerably more within its mortared stone walls than the average churchyard. Measuring roughly 115 metres east to west and 65 metres north to south, the sub-rectangular enclosure contains a high cross, a round tower, a cathedral, scattered architectural fragments, burials running from early medieval times up to the modern era, and, tucked quietly to the east of the cathedral, two small stone structures that most visitors walk past without a second glance.

Scholarship by Bradley and colleagues in 1986 suggested that this walled enclosure may represent the innermost precinct of St. Brigid's monastery, the famous early Christian foundation that gave the town much of its identity and its name, Cill Dara, meaning church of the oak. That monastic origin would make the boundary wall far more than a tidy Victorian addition; it could be tracing a boundary laid out well over a millennium ago. Within the enclosure, to the north-east of the cathedral, the low footings of two walls are thought to be the remains of a mortuary chapel associated with the Leigh family. More unusual still are the two small structures immediately east of the cathedral. The first is a barrel-vaulted chamber, roughly 4.3 metres long and 3.1 metres wide, built using wicker centring, a technique in which woven wickerwork provided the temporary mould over which the stone vault was laid, and which leaves a distinctive impression in the finished stonework. Originally standing above ground, it retains a lintelled opening in its south wall that splays inward. Just north of it sits an even smaller subterranean chamber, only about 1.5 metres by 1.4 metres, with a stone roof, and interpreted as a possible burial vault. Neither structure advertises itself, and neither carries a label explaining what it might be.