  We report the discovery of Zr$_3$Ir as a new type of unconventional
noncentrosymmetric superconductor (with $T_c = 2.3$ K), here investigated
mostly via muon-spin rotation/relaxation ($\mu$SR) techniques. Its
superconductivity was characterized using magnetic susceptibility, electrical
resistivity, and heat capacity measurements. The low-temperature superfluid
density, determined via transverse-field $\mu$SR and electronic specific heat,
suggests a fully-gapped superconducting state. The spontaneous magnetic fields,
revealed by zero-field $\mu$SR below $T_c$, indicate the breaking of
time-reversal symmetry in Zr$_3$Ir and, hence, the unconventional nature of its
superconductivity. By using symmetry arguments and electronic-structure
calculations we obtain a superconducting order parameter that is fully
compatible with the experimental observations. Hence, our results clearly
suggest that Zr$_3$Ir represents a new member of noncentrosymmetric
superconductors with broken time-reversal symmetry.
