  Fully frustrated one-dimensional diamond Josephson chains have been shown [B.
Dou\c{c}ot and J. Vidal, Phys. Rev. Lett. {\bf 88}, 227005 (2002)] to posses a
remarkable property: The superfluid phase occurs through the condensation of
pairs of Cooper pairs. By means of Monte Carlo simulations we analyze
quantitatively the Insulator to $4e$-Superfluid transition. We determine the
location of the critical point and discuss the behaviour of the phase-phase
correlators. For comparison we also present the case of a diamond chain at zero
and 1/3 frustration where the standard $2e$-condensation is observed.
