  The development of sensitive cryogenic light detectors is of primary interest
for bolometric experiments searching for rare events like dark matter
interactions or neutrino-less double beta decay. Thanks to their good energy
resolution and the natural multiplexed read-out, Kinetic Inductance Detectors
(KIDs) are particularly suitable for this purpose. To efficiently couple
KIDs-based light detectors to the large crystals used by the most advanced
bolometric detectors, active surfaces of several cm$^2$ are needed. For this
reason, we are developing phonon-mediated detectors. In this paper we present
the results obtained with a prototype consisting of four 40 nm thick aluminum
resonators patterned on a 2$\times$2 cm$^2$ silicon chip, and calibrated with
optical pulses and X-rays. The detector features a noise resolution
$\sigma_E=154\pm7$ eV and an (18$\pm$2)$\%$ efficiency.
