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We prove an LDP for the empirical measure of complex zeros of a Gaussianrandom complex polynomial of degree N of one variable as N tends to infinity.The Gaussian measure is induced by an inner product defined by a smooth weight(Hermitian metric) $h$ and a Bernstein-Markov measure $\nu$. The speed is N^2and the the unique minimizer of the rate function $I$ is the weightedequilibrium measure $\nu_{h, K}$ with respect to $h$ on the support $K$ of$\nu$.

Large deviations of empirical zero point measures on Riemann surfaces, I: $g = 0$