The materials Cr1/3MS2 (M=Nb, Ta) have recently attracted attention as potential hosts of a chiral magnetic soliton lattice (CSL), with confirmed observations of this state in the M=Nb material. Magnetic solitons show a potential for applications in future data-transfer applications. Our previous LF-muSR work on topological magnetic textures such as skyrmions has shown that the technique provides unique insights into the nature of these states. Here we propose to perform the first LF-muSR measurements of a CSL state. This proposal is part of a major UK project to investigate skyrmion physics, along with related topological physics, and to engineer topological materials towards application.