  Heavy atomic nuclei have an excess of neutrons over protons, which leads to
the formation of a neutron skin whose thickness is sensitive to details of the
nuclear force. This links atomic nuclei to properties of neutron stars, thereby
relating objects that differ in size by orders of magnitude. The nucleus
${}^{208}$Pb is of particular interest because it exhibits a simple structure
and is experimentally accessible. However, computing such a heavy nucleus has
been out of reach for ab initio theory. By combining advances in quantum
many-body methods, statistical tools, and emulator technology, we make
quantitative predictions for the properties of ${}^{208}$Pb starting from
nuclear forces that are consistent with symmetries of low-energy quantum
chromodynamics. We explore $10^9$ different nuclear-force parameterisations via
history matching, confront them with data in select light nuclei, and arrive at
an importance-weighted ensemble of interactions. We accurately reproduce bulk
properties of ${}^{208}$Pb and determine the neutron skin thickness, which is
smaller and more precise than a recent extraction from parity-violating
electron scattering but in agreement with other experimental probes. This work
demonstrates how realistic two- and three-nucleon forces act in a heavy nucleus
and allows us to make quantitative predictions across the nuclear landscape.
