A laboratory for measuring low-level radioactivity has been built at the AlbaNova University Center in Stockholm. Low-level concrete in combination with a 5 cm iron lining provide an average photon fluency rate from terrestrial sources at least a factor of 40 below that in the common laboratories of the Center. The radon activity inside the laboratory has been measured to (3+/-2) Bq m(-3). Material considerations are discussed. Construction and performance of the laboratory, as well as the present instrumentation, is described.