  We present low temperature transport measurements in one dimensional
Josephson junctions rhombi chains. We have measured the current phase relation
of a chain of 8 rhombi. The junctions are either in the classical phase regime
with the Josephson energy much larger than the charging energy, $E_{J}\gg
E_{C}$, or in the quantum phase regime where $E_{J}/E_{C}\approx 2$. In the
strong Josephson coupling regime ($E_{J}\gg E_{C} \gg k_{B}T$) we observe a
sawtooth-like supercurrent as a function of the phase difference over the
chain. The period of the supercurrent oscillations changes abruptly from one
flux quantum $\Phi_{0}$ to half the flux quantum $\Phi_{0}/2$ as the rhombi are
tuned in the vicinity of full frustration. The main observed features can be
understood from the complex energy ground state of the chain. For
$E_{J}/E_{C}\approx 2$ we do observe a dramatic suppression and rounding of the
switching current dependence which we found to be consistent with the model
developed by Matveev et al.(Phys. Rev. Lett. {\bf 89}, 096802(2002)) for long
Josephson junctions chains.
