A new and distinct variety of nectarine tree (Prunus persica sub species nuciperisica), and which is denominated varietally as ‘Burnectthirty’, and which further produces an attractively colored yellow-fleshed, non-melting, acidic clingstone nectarine, which is mature for harvesting and shipment approximately May 18 to May 25 under ecological conditions prevailing in the San Joaquin Valley of central California.