  The discovery of the Higgs boson with its mass around 125 GeV by the ATLAS
and CMS Collaborations marked the beginning of a new era in high energy
physics. The Higgs boson will be the subject of extensive studies of the
ongoing LHC program. At the same time, lepton collider based Higgs factories
have been proposed as a possible next step beyond the LHC, with its main goal
to precisely measure the properties of the Higgs boson and probe potential new
physics associated with the Higgs boson. The Circular Electron Positron
Collider~(CEPC) is one of such proposed Higgs factories. The CEPC is an
$e^+e^-$ circular collider proposed by and to be hosted in China. Located in a
tunnel of approximately 100~km in circumference, it will operate at a
center-of-mass energy of 240~GeV as the Higgs factory. In this paper, we
present the first estimates on the precision of the Higgs boson property
measurements achievable at the CEPC and discuss implications of these
measurements.
