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The Compact Linear Collider is one of the two main European options for a collider in a post Large Hadron Collider era. This is a linear $e^+e^-$ collider with three centre-of-mass energy stages: 380 GeV, 1.5 TeV and 3 TeV. The luminosity performance of the first stage at 380 GeV is presented including the impact of static and dynamic imperfections. These calculations are performed with fully realistic tracking simulations from the exit of the damping rings to the interaction point and including beam-beam effects in the collisions. A luminosity of $4.3\times10^{34}\,\text{cm}^{-2}\text{s}^{-1}$ can be achieved with a perfect collider, which is almost three times the nominal luminosity target of $1.5\times10^{34}\,\text{cm}^{-2}\text{s}^{-1}$. In simulations with static imperfections, a luminosity of $2.35\times10^{34}\,\text{cm}^{-2}\text{s}^{-1}$ or greater is achieved by 90% of randomly misaligned colliders. Expressed as a percentage of the nominal luminosity target, this is a surplus of approximately 57%. Including the impact of ground motion, a luminosity surplus of 53% or greater can be expected for 90% of colliders. The average expected luminosity is $2.8\times10^{34}~\text{cm}^{-2}\text{s}^{-1}$, which is almost twice the nominal luminosity target.