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Westerlund 1 (Wd1) is potentially the largest star cluster in the Galaxy. That designation critically depends upon the distance to the cluster, yet the cluster is highly obscured, making luminosity-based distance estimates difficult. Using Gaia Data Release 2 (DR2) parallaxes and Bayesian inference, we infer a parallax of $0.35^{+0.07}_{-0.06}$ mas corresponding to a distance of $2.6^{+0.6}_{-0.4}$ kpc. To leverage the combined statistics of all stars in the direction of Wd1, we derive the Bayesian model for a cluster of stars hidden among Galactic field stars; this model includes the parallax zero-point. Previous estimates for the distance to Wd1 ranged from 1.0 to 5.5 kpc, although values around 5 kpc have usually been adopted. The Gaia DR2 parallaxes reduce the uncertainty from a factor of 3 to 18 per cent and rules out the most often quoted value of 5 kpc with 99 per cent confidence. This new distance allows for more accurate mass and age determinations for the stars in Wd1. For example, the previously inferred initial mass at the main-sequence turn-off was around 40 M⊙; the new Gaia DR2 distance shifts this down to about 22 M⊙. This has important implications for our understanding of the late stages of stellar evolution, including the initial mass of the magnetar and the LBV in Wd1. Similarly, the new distance suggests that the total cluster mass is about four times lower than previously calculated.