  Quantum physics in one spatial dimension is remarkably rich, yet even with
strong interactions and disorder, surprisingly tractable. This is due to the
fact that the low-energy physics of nearly all one-dimensional systems can be
cast in terms of the Luttinger liquid, a key concept that parallels that of the
Fermi liquid in higher dimensions. Although there have been many theoretical
proposals to use linear chains and ladders of Josephson junctions to create
novel quantum phases and devices, only modest progress has been made
experimentally. One major roadblock has been understanding the role of disorder
in such systems. We present experimental results that establish the insulating
state of linear chains of sub-micron Josephson junctions as Luttinger liquids
pinned by random offset charges, providing a one-dimensional implementation of
the Bose glass, strongly validating the quantum many-body theory of
one-dimensional disordered systems. The ubiquity of such an electronic glass in
Josephson-junction chains has important implications for their proposed use as
a fundamental current standard, which is based on synchronisation of coherent
tunnelling of flux quanta (quantum phase slips).
