The TLL phase is a quantum spin condensed state in the one-dimensional system. In the case of DIMPY system which is a quasi-one-dimensional organic magnet, the TLL phase is induced by the magnetic field forming a sea of the singlet spin state with some excited triplet spins. The µSR measurement successfully picks up the spin-relaxation behavior in the TLL phase in this system. Our target system to study the TLL state is the CsO2 which is one of superoxides series which we are currently working to investigate magnetic properties of magnetic moment on the O2 dumbbell. It is recently reported from NMR measurement that the TLL phase is realized in this system also below about 30 K down to TN~9 K. Since the µSR study in the DIMPY system is well working on the TLL phase, we follow the similar measurement on CsO2. We try to achieve more accurate information on the TLL phase rather than NMR.