One of the most intriguing puzzles in biology is the degree to which evolution is repeatable. The repeatability of evolution, or parallel evolution, has been studied in a variety of model systems, but has rarely been investigated with clinically relevant viruses. To investigate parallel evolution of HIV-1, we passaged two replicate HIV-1 populations for almost one year in each of two human T-cell lines. For each of the four evolution lines, we determined the genetic composition of the viral population at nine time points by deep sequencing the entire genome. Mutations that were carried by the majority of the viral population accumulated continuously over one year in each evolution line. Many majority mutations appeared in more than one evolution line, i.e. our experiments showed an extreme degree of parallel evolution. In one of the evolution lines, 62% of the majority mutations also occur in another line. The parallelism impairs our ability to reconstruct the evolutionary history by phylogenetic methods. We show that one can infer the correct phylogenetic topology by including minority mutations in our analysis. We also find that mutation diversity at the beginning of the experiment is predictive of the frequency of majority mutations at the end of the experiment.