Motivated by the controversy over the surface metallicity of the Sun, we present a re-analysis of the solar photospheric oxygen (O) abundance. New atomic models of O and Ni are used to perform non-local thermodynamic equilibrium (NLTE) calculations with 1D hydrostatic (MARCS) and 3D hydrodynamical (Stagger and Bifrost) models. The Bifrost 3D MHD simulations are used to quantify the influence of the chromosphere. We compare the 3D NLTE line profiles with new high-resolution, R≈700000≈700000⁠, spatially resolved spectra of the Sun obtained using the IAG FTS instrument. We find that the O I lines at 777 nm yield the abundance of log A(O) = 8.74 ± 0.03 dex, which depends on the choice of the H-impact collisional data and oscillator strengths. The forbidden [O I] line at 630 nm is less model dependent, as it forms nearly in LTE and is only weakly sensitive to convection. However, the oscillator strength for this transition is more uncertain than for the 777 nm lines. Modelled in 3D NLTE with the Ni I blend, the 630 nm line yields an abundance of log A(O) = 8.77 ± 0.05 dex. We compare our results with previous estimates in the literature and draw a conclusion on the most likely value of the solar photospheric O abundance, which we estimate at log A(O) = 8.75 ± 0.03 dex.