  We present the first determination of the binding energy of the $H$ dibaryon
in the continuum limit of lattice QCD. The calculation is performed at five
values of the lattice spacing $a$, using O($a$)-improved Wilson fermions at the
SU(3)-symmetric point with $m_\pi=m_K\approx 420$ MeV. Energy levels are
extracted by applying a variational method to correlation matrices of bilocal
two-baryon interpolating operators computed using the distillation technique.
Our analysis employs L\"uscher's finite-volume quantization condition to
determine the scattering phase shifts from the spectrum and vice versa, both
above and below the two-baryon threshold. We perform global fits to the lattice
spectra using parametrizations of the phase shift, supplemented by terms
describing discretization effects, then extrapolate the lattice spacing to
zero. The phase shift and the binding energy determined from it are found to be
strongly affected by lattice artifacts. Our estimate of the binding energy in
the continuum limit of three-flavor QCD is $B_H=3.97\pm1.16_{\rm
stat}\pm0.86_{\rm syst}$ MeV.
