We report measurements of the longitudinal ( 139 T −1 1 ) and transverse ( 139 T −1 2 ) decay rates of the magnetization of 139 La nuclei performed in a high quality single crystal of La1.65Eu0.2Sr0.15CuO4. We observe a dramatic slowing of the Cu 3d spins manifested as a sharp increase of both 139 T −1 1 and 139 T −1 2 below 30 K. We find that in this temperature range the fluctuations involve a unique time scale τ which diverges as (T − TA) −1.9 with TA ≈ 5 K. This behavior is distinct from the continuous freezing observed in underdoped La1−xSrxCuO4 which involves a distribution of energy barriers. By contrast, in La1.65Eu0.2Sr0.15CuO4, the freezing below 30K is intrinsic to its magnetic ground state and the observed power law supports the existence of a glass forming "charge stripe liquid".Charge inhomogeneities in doped transition metaloxides have aroused great interest because of their possible implication in superconductivity. Indeed, it has been proposed [1,2,3,4] that the superconducting state in underdoped cuprates may consist of a charge stripe phase, in which hole-rich fluctuating stripes act as antiphase boundaries between undoped antiferromagnetic (AF) domains. Experimentally, the presence of a stripe order was inferred from elastic neutron scattering measurements [5] in compounds that are not superconducting: doped lanthanum nickelates and the rare earth codoped lanthanum cuprate La 1.48 Nd 0.4 Sr 0.12 CuO 4 . In the latter, the substitution for La ions by isovalent rare earth ions (Nd or Eu) induces a structural transition from the low temperature orthorhombic (LTO) to the low temperature tetragonal (LTT) phase in which a magnetic ground state occurs in lieu of the superconducting state [6].In both structures, LTO and LTT, the CuO 6 octahedra are tilted inducing a staggered buckling of the CuO 2 plane [7]. The difference between the two phases consists only of a rotation of the tilt axis from [110] HTT in the LTO phase to [100] HTT or [010] HTT alternating along the c axis in the LTT phase. Though specific to lanthanum cuprates, the LTT structure was shown [6,8] to have the remarkable property of generating either a magnetic or superconducting ground state with similar critical temperature at fixed optimal Sr 2+ doping (x=0.15) depending only on the amplitude of the buckling, controlled by the Eu or Nd concentration. This suggests the same physics underlies the two outcomes, but little is known about the fundamental mechanism that connects them. In this context, it is important to gain further insight into the low energy properties of the magnetic ground state in rare earth co-doped lanthanum cuprates.In this Letter, we report NMR measurements performed on 63 Cu and 139 La nuclei in a La 1.65 Eu 0.2 Sr 0.15 CuO 4 single crystal. For the first time, we investigate the slowing down of the Cu 3d spins in this compound by measuring two relaxation rates: 139 T −1 1 and 139 T −1 2 . For a given orientation of the crystal in a static field H 0 , T −1 1 probes the spectral weight of the transverse fluctuati...