The influence of added disklike synthetic clay particles (Laponite RDS) on the rheology and structure of the hexagonal phase formed by the poly(oxyethylene)-poly(oxypropylene) -poly(oxyethylene) triblock copolymer Pluronic P123 was investigated by dynamic shear rheometry and smallangle X-ray scattering (SAXS). The dimensions of the Laponite RDS particles were determined by analysis of the SAXS form factor, measured in dilute solution. The dynamic shear modulus of gels of P123 is found to be essentially independent of the amount of Laponite RDS up to an added Laponite solution concentration of 9 wt%, above which gelation of Laponite solutions is observed. SAXS shows that addition of Laponite particles drives a transition from a hexagonal phase of rodlike micelles at low temperature to a lamellar phase at high temperature. The transition temperature decreases as a function of the amount of added Laponite, in contrast to the width of the coexistence region between the two structures which remains nearly constant. The formation of a lamellar phase is rationalized on the basis of the entropically favored packing of the Laponite disks. The disks are found to be intercalated between the lamellae, the separation between them decreasing as Laponite concentration increases.