  In this paper, we established the Freidlin-Wentzell type large deviation
principles for first-order scalar conservation laws perturbed by small
multiplicative noise. Due to the lack of the viscous terms in the stochastic
equations, the kinetic solution to the Cauchy problem for these first-order
conservation laws is studied. Then, based on the well-posedness of the kinetic
solutions, we show that the large deviations holds by utilising the weak
convergence approach.
