  We study Bose-Einstein condensation (BEC) in the Luttinger-Sy model. Here,
Bose point particles in one spatial dimension do not interact with each other,
but, through a positive (repulsive) point potential with impurities which are
randomly located along the real line according to the points of a Poisson
process. Our emphasis is on the case in which the interaction strength is not
infinite. As a main result, we prove that in thermal equilibrium the
one-particle ground state is macroscopically occupied, provided that the
particle density is larger than a critical one depending on the temperature.
