A chiral superconductor has been proposed as one pathway to realize topological quantum computation utilizing the predicted Majorana normal fluid at its boundary (i.e., a point, edge, or surface). The search for experimental realizations has led to the discovery of 1D chiral superconducting systems. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here we report evidence for a chiral spin-triplet pairing state of UTe$_2$ with significant surface normal fluid response. The microwave surface impedance of the UTe$_2$ crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity in the zero temperature limit supports the presence of a significant normal fluid response. The superfluid conductivity follows the low temperature behavior predicted for the axial spin-triplet state, which is further narrowed down to the chiral spin-triplet state with evidence of broken time-reversal symmetry. The temperature dependence of the superfluid conductivity also reveals a low bulk impurity scattering rate and low frequency-to-energy-gap ratio, implying that the observed normal fluid response does not have a trivial origin. Our findings suggest that UTe$_2$ can be a new platform to study exotic topological excitations in higher dimension, and may play the role of a versatile 3D building block in the future era of topological quantum computation.
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