In superconductors, the inversion symmetry of the crystallographic structure plays a central role in the formation of the Cooper pairs. When inversion symmetry is broken, there is the possibility of a mixing of singlet-triplet pairing, leading to unconventional superconducting properties.La7Ir3 is a noncentrosymmetric (NCS) superconductor where time-reversal symmetry (TRS) breaking below the superconducting Tc is observed in polycrystalline samples. We have successfully grown the first single crystals of La7Ir3. We propose to use muons to study the anisotropy of the superconducting properties of La7Ir3, investigate the influence of magnetic fluctuations, and search for TRS breaking. To the best of our knowledge, this would be the first time TRS breaking is studied in a single crystal of a NCS superconductor where TRS breaking is observed in samples in the polycrystalline form.