We have developed a new Linear Support Vector Machine (SVM) training algorithm called OCAS. Its computational effort scales linearly with the sample size. In an extensive empirical evaluation OCAS significantly outperforms current state of the art SVM solvers, like SVMLight, SVMPerf and BMRM, achieving speedups of over 1,000 on some datasets over SVMLight and 20 over SVMPerf, while obtaining the same precise Support Vector solution. OCAS even in the early optimization steps shows often faster convergence than the so far in this domain prevailing approximative methods SGD and Pegasos. Effectively parallelizing OCAS we were able to train on a dataset of size 15 million examples (itself about 32GB in size) in just 671 seconds --- a competing string kernel SVM required 97,484 seconds to train on 10 million examples sub-sampled from this dataset.