  Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin
liquid without time-reversal symmetry, and it is considered as the parent state
of an exotic type of superconductivity--anyon superconductor. Such exotic state
has been sought for more than twenty years, however it remains unclear whether
it can exist in realistic system where time-reversal symmetry is breaking
(T-breaking) spontaneously. By using the density matrix renormalization group,
we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model
(KHM), which has spontaneously T-breaking. We find that our model has two
topological degenerate ground states, which exhibit non-vanishing scalar
chirality order and are protected by finite excitation gap. Further, we
identify this state as KL CSL by the characteristic edge conformal field theory
from the entanglement spectrum and the quasiparticles braiding statistics
extracted from the modular matrix. We also study how this CSL phase evolves as
the system approaches the nearest neighbor KHM.
