This thesis presents experiments on degenerate Bose gases in the quasi-one dimensional regime. For this purpose we use an atom chip, microfabricated wires deposited on surfaces, to create very anisotropic traps in which we measured the statistical properties of an ultracold bosonic gas (Rubidium 87). For a classical gas, where the particles are statistically independent, density fluctuations are given by the atomic shot noise. At lower temperatures, the quantum nature of the particles appears (indistinguishable bosons), and an extra term has to be taken into account to describe the bosonic bunching. At low atomic densities, we observe these two kinds of behavior in good agreement with the ideal Bose gas predictions. At higher atomic densiti...