  We consider the 1d CFT defined by the half-BPS Wilson line in planar
$\mathcal{N}=4$ super Yang-Mills. Using analytic bootstrap methods we derive
the four-point function of the super-displacement operator at fourth order in a
strong coupling expansion. Via AdS/CFT, this corresponds to the first
three-loop correlator in AdS ever computed. To do so we address the operator
mixing problem by considering a family of auxiliary correlators. We further
extract the anomalous dimension of the lightest non-protected operator and find
agreement with the integrability-based numerical result of Grabner, Gromov and
Julius.
