We present results of a detailed study of X-ray flaring in the Z-track source Sco X-1 in a highly super-Eddington state made using high quality Rossi-XTE data from the PCA and HEXTE instruments . The emission model successfully used to explain the dipping LMXB , and other classes of LMXB in recent years , was applied to study the physical evolution along the Z-track which remains a major problem . This model consists of blackbody emission from the neutron star plus Comptonized emission from an extended accretion disk corona . As found in earlier work , major changes take place in the neutron star blackbody emission with kT increasing in flaring , and the blackbody radius R _ { BB } increasing substantially to a maximum value of 9.4 \pm 0.6 km , consistent with the radius of the neutron star , after which R _ { BB } decreases . Thus this result is a measurement of neutron star radius . The behaviour of Sco X-1 in flaring is compared with our previous results for the strong flaring that takes place in the bright dipping , flaring LMXB X 1624-490 . Remarkably , during movement along the Normal Branch towards the apex with the Flaring Branch , the luminosities of both spectral components decrease , suggesting the possibility that \dot { M } may decrease on the Normal Branch , contrary to the widely-held view that \dot { M } increases monotonically along the Z-track . During flaring , we detect for the first time an increase of the Comptonization cut-off energy which may suggest heating of the ADC plasma by the neutron star flare . The energy of a broad Gaussian line at \sim 6.4 keV does not change , but the intensity of the line increases in flaring suggesting either an increase in ADC size in flaring or the effects of irradiation by the neutron star .