A Large Size air Cherenkov Telescope (LST) prototype, proposed for the Cherenkov Telescope Array, is under construction at the Canarian Island of La Palma (Spain) this year. The LST camera, which comprises of an array of photomultipliers (PMTs), requires a precise and regular calibration over a large dynamic range. We present a system built to provide the optical calibration of the camera consisting of a pulsed laser (355 nm wavelength, 400 ps pulse width), a set of filters to guarantee a large dynamic range of photons on the sensors, and a diffusing sphere to uniformly spread the laser light , with flat fielding within 3%, over the camera plane at 28 m away. The prototype of the system developed at INFN, designed to calibrate each individual PMT up to 103 photoelectrons, is hermetically closed and filled with dry air to make the system completely isolated from the external environment. In the paper we present the results of the tests for the evaluation of the photon density at the camera plane, the system isolation from the environment, and the shape of the signal as detected by the PMTs. The description of the communication of the system with the rest of detector is also given.