The oldest known archaeological site in Ireland is a Dolmen in the Burren in County Clare, estimated to be around 5,800 years old. The Poulnabrone Dolmen is a single-chamber portal tomb made of limestone. Excavations of the site found human remains of both adults and children as well as various stone and bone objects.   It appears that none of the 30 or so people buried there were related. 

From a distance, it looks like a large picnic table with a top stone (capstone) and legs (portal stones).   When constructed, it would have been covered with soil and capped by a cairn.

Ireland has over 170 Dolmens.

If visiting the Cliffs of Moher, consider adding this as a site to visit.

Further information about the Poulnabrone Dolmen can be found here.

More information on megalithic burial chambers can be found here.  It has some interesting DNA results.