  Spontaneous symmetry-breaking quantum phase transitions play an essential
role in condensed matter physics. The collective excitations in the
broken-symmetry phase near the quantum critical point can be characterized by
fluctuations of phase and amplitude of the order parameter. The phase
oscillations correspond to the massless Nambu$-$Goldstone modes whereas the
massive amplitude mode, analogous to the Higgs boson in particle physics, is
prone to decay into a pair of low-energy Nambu$-$Goldstone modes in low
dimensions. Especially, observation of a Higgs amplitude mode in two dimensions
is an outstanding experimental challenge. Here, using the inelastic neutron
scattering and applying the bond-operator theory, we directly and unambiguously
identify the Higgs amplitude mode in a two-dimensional S=1/2 quantum
antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$ near a quantum critical point in two
dimensions. Owing to an anisotropic energy gap, it kinematically prevents such
decay and the Higgs amplitude mode acquires an infinite lifetime.
