  The kagome lattice, the most prominent structural motif in quantum physics,
benefits from inherent nontrivial geometry to host diverse quantum phases,
ranging from spin-liquid phases, topological matter to intertwined orders, and
most rarely unconventional superconductivity. Recently, charge sensitive probes
have suggested that the kagome superconductors AV_3Sb_5 (A = K, Rb, Cs) (A = K,
Rb, Cs) exhibit unconventional chiral charge order, which is analogous to the
long-sought-after quantum order in the Haldane model or Varma model. However,
direct evidence for the time-reversal symmetry-breaking of the charge order
remains elusive. Here we utilize muon spin relaxation to probe the kagome
charge order and superconductivity in KV_3Sb_5. We observe a striking
enhancement of the internal field width sensed by the muon ensemble, which
takes place just below the charge ordering temperature and persists into the
superconducting state. Remarkably, the muon spin relaxation rate below the
charge ordering temperature is substantially enhanced by applying an external
magnetic field. We further show the multigap nature of superconductivity in
KV_3Sb_5 and that the T_c/lambda_{ab}^{-2} ratio is comparable to those of
unconventional high-temperature superconductors. Our results point to
time-reversal symmetry breaking charge order intertwining with unconventional
superconductivity in the correlated kagome lattice.
