We present high resolution ($\sim0.14$" = 710 pc) ALMA [CII] 158$\mu$m anddust continuum follow-up observations of REBELS-25, a [CII]-luminous($L_{\mathrm{[CII]}}=(1.7\pm0.2)\times 10^9 \mathrm{L_{\odot}}$) galaxy atredshift $z=7.3065\pm0.0001$. These high resolution, high signal-to-noiseobservations allow us to study the sub-kpc morphology and kinematics of thismassive ($M_* = 8^{+4}_{-2} \times 10^9 \mathrm{M_{\odot}}$) star-forming(SFR$_{\mathrm{UV+IR}} = 199^{+101}_{-63} \mathrm{M_{\odot}} \mathrm{yr}^{-1}$)galaxy in the Epoch of Reionisation. By modelling the kinematics with$^{\mathrm{3D}}$BAROLO, we find it has a low velocity dispersion ($\bar{\sigma}= 33 \pm 9$ km s$^{-1}$) and a high ratio of ordered-to-random motion($V_{\mathrm{rot, ~max}}/\bar{\sigma} = 11 ^{+8}_{-4}$), indicating thatREBELS-25 is a dynamically cold disc. Additionally, we find that the [CII]distribution is well fit by a near-exponential disc model, with a S\'ersicindex, $n$, of $1.3 \pm 0.2$, and we see tentative evidence of more complexnon-axisymmetric structures suggestive of a bar in the [CII] and dust continuumemission. By comparing to other high spatial resolution cold gas kinematicstudies, we find that dynamically cold discs seem to be more common in the highredshift Universe than expected based on prevailing galaxy formation theories,which typically predict more turbulent and dispersion-dominated galaxies in theearly Universe as an outcome of merger activity, gas accretion and more intensefeedback. This higher degree of rotational support seems instead to beconsistent with recent cosmological simulations that have highlighted thecontrast between cold and warm ionised gas tracers, particularly for massivegalaxies. We therefore show that dynamically settled disc galaxies can form asearly as 700 Myr after the Big Bang.