We present an efficient algorithm for the problem of online multiclass prediction with bandit feedback in the fully adversarial setting. We measure its regret with respect to the log-loss defined in (Abernethy and Rakhlin, 2009), which is parameterized by a scalar \(\alpha\). We prove that the regret of Newtron is \(O(\log T)\) when \(\alpha\) is a constant that does not vary with horizon \(T\), and at most \(O(T^{2/3})\) if \(\alpha\) is allowed to increase to infinity with \(T\). For \(\alpha = O(\log T)\), the regret is bounded by \(O(\sqrt{T})\), thus solving the open problem of Kakade et al (2008) and Abernethy and Rakhlin (2009). Our algorithm is based on a novel application of the online Newton method (Hazan et al, 2007). We test our algorithm and show it to perform well in experiments, even when \(\alpha\)  is a small constant.