(1) Background: Histone deacetylases (HDACs) play a critical role in epigenetic signaling in cancer; however, available HDAC inhibitors have limited therapeutic windows and suboptimal pharmacokinetics (PK). This first-in-human phase I dose escalation study evaluated the safety, PK, pharmacodynamics (PDx), and efficacy of the oral Class I-targeting HDAC inhibitor bocodepsin (OKI-179). (2) Patients and Methods: Patients (n = 34) with advanced solid tumors were treated with OKI-179 orally once daily in three schedules: 4 days on 3 days off (4:3), 5 days on 2 days off (5:2), or continuous in 21-day cycles until disease progression or unacceptable toxicity. Single-patient escalation cohorts followed a standard 3 + 3 design. (3) Results: The mean duration of treatment was 81.2 (range 11–447) days. The most frequent adverse events in all patients were nausea (70.6%), fatigue (47.1%), and thrombocytopenia (41.2%). The maximum tolerated dose (MTD) of OKI-179 was 450 mg with 4:3 and 200 mg with continuous dosing. Dose-limiting toxicities included decreased platelet count and nausea. Prolonged disease control was observed, including two patients with platinum-resistant ovarian cancer. Systemic exposure to the active metabolite exceeded the preclinical efficacy threshold at doses lower than the MTD and was temporally associated with increased histone acetylation in circulating T cells. (4) Conclusions: OKI-179 has a manageable safety profile at the recommended phase 2 dose (RP2D) of 300 mg daily on a 4:3 schedule with prophylactic oral antiemetics. OKI-179 is currently being investigated with the MEK inhibitor binimetinib in patients with NRAS-mutated melanoma in the phase 2 Nautilus trial.