Inter-modal phase-matched third harmonic generation has been demonstrated in an exposed-core microstructured optical fiber. Our fiber, with a partially open core having a diameter of just 1.85 µm, shows efficient multi-peak third-harmonic generation between 500 nm and 530 nm, with a maximum visible-wavelength output of 0.96 μW. Mode images and simulations show strong agreement, confirming the phase-matching process and polarization dependence. We anticipate this work will lead to tailorable and tunable visible light sources by exploiting the open access to the optical fiber core, such as depositing thin-film coatings in order to shift the phase matching conditions.