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The Large Magellanic Cloud (LMC) is the closest and most studied example of an irregular galaxy. Among its principal defining morphological features, its off-centred bar and single spiral arm stand out, defining a whole family of galaxies known as the Magellanic spirals (Sm). These structures are thought to be triggered by tidal interactions and possibly maintained via gas accretion. However, it is still unknown whether they are long-lived stable structures. In this work, by combining photometry that reaches down to the oldest main sequence turn-off in the colour-magnitude diagrams (CMD, up to a distance of $\sim$4.4 kpc from the LMC centre) from the SMASH survey and CMD fitting techniques, we find compelling evidence supporting the long-term stability of the LMC spiral arm, dating the origin of this structure to more than 2~Gyr ago. The evidence suggests that the close encounter between the LMC and the Small Magellanic Cloud (SMC) that produced the gaseous Magellanic Stream and its Leading Arm (LA) also triggered the formation of the LMC's spiral arm. Given the mass difference between the Clouds and the notable consequences of this interaction, we can speculate that this should have been one of their closest encounters. These results set important constraints on the timing of LMC-SMC collisions, as well as on the physics behind star formation induced by tidal encounters.