The genetic defect in Friedreich's ataxia (FRDA) is the hyperexpansion of a GAA•TTC triplet in the first intron of the FXN gene, encoding the essential mitochondrial protein frataxin. Histone post-translational modifications near the expanded repeats are consistent with heterochromatin formation and consequent FXN gene silencing. Using a newly developed human neuronal cell model, derived from patient-induced pluripotent stem cells, we find that 2-aminobenzamide histone deacetylase (HDAC) inhibitors increase FXN mRNA levels and frataxin protein in FRDA neuronal cells. However, only compounds targeting the class I HDACs 1 and 3 are active in increasing FXN mRNA in these cells. Structural analogs of the active HDAC inhibitors that selectively target either HDAC1 or HDAC3 do not show similar increases in FXN mRNA levels. To understand the mechanism of action of these compounds, we probed the kinetic properties of the active and inactive inhibitors, and found that only compounds that target HDACs 1 and 3 exhibited a slow-on/slow-off mechanism of action for the HDAC enzymes.