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Hybrid semiconductor-superconductor InAs-Al nanowires with uniform and defect-free crystal interfaces are one of the most promising candidates used in the quest for Majorana zero modes (MZMs). However, InAs nanowires often exhibit a high density of randomly distributed twin defects and stacking faults, which result in an uncontrolled and non-uniform InAs-Al interface. Furthermore, this type of disorder can create potential inhomogeneity in the wire, destroy the topological gap, and form trivial sub-gap states mimicking MZM in transport experiments. Further study shows that reducing the InAs nanowire diameter from growth can significantly suppress the formation of these defects and stacking faults. Here, we demonstrate the in situ growth of ultra-thin InAs nanowires with epitaxial Al film by molecular-beam epitaxy. Our InAs diameter (~ 30 nm) is only one-third of the diameters (~ 100 nm) commonly used in literatures. The ultra-thin InAs nanowires are pure phase crystals for various different growth directions, suggesting a low level of disorder. Transmission electron microscopy confirms an atomically sharp and uniform interface between the Al shell and the InAs wire. Quantum transport study on these devices resolves a hard induced superconducting gap and $2e^-$ periodic Coulomb blockade at zero magnetic field, a necessary step for future MZM experiments. A large zero bias conductance peak with a peak height reaching 80% of $2e^2/h$ is observed.