A 3.9 GPA is above Ohio University's admitted middle-50% GPA range of 3.35–3.85.
You're competitive on GPA — at a school this selective the rest of your application (rigor, essays, extracurriculars, and spikes) is what decides it.
A GPA is the single biggest academic factor, but it's necessary, not sufficient — especially at a 85.2%-acceptance school like Ohio University. Your test scores, course rigor, extracurriculars, essays, and any standout achievements all move the number. The estimate above assumes typical scores and rigor; your real odds depend on your full profile.
Estimates are CDS-based and for a typical applicant. Run your full profile for your real, calibrated odds.