Cygnus X-2 is one of the brightest and longest known X-ray sources. We present high resolution optical spectroscopy of Cyg X-2 obtained over 4 years which gives an improved mass function of 0.69 +/- 0.03 solar mass(1sigma). In addition, we resolve the rotationally broadened absorption features of the secondary star for the first time, deriving a rotation speed of v sin i = 34.2 +/- 2.5 km/s (1sigma) which leads to a mass ratio of q = Mc/Mx = 0.34 +/- 0.04 (1sigma, assuming a tidally-locked and Roche lobe-filling secondary). Hence with the lack of X-ray eclipses (i.e. i less than or approximately equals 73 deg) we can set firm 95% confidence lower limits to the neutron star mass of Mx greater than 1.27 solar mass and to the companion star mass of Mc greater than 0.39 solar mass. However, by additionally requiring that the companion must exceed 0.75 solar mass (as required theoretically to produce a steady low-mass X-ray binary), then Mx greater than 1.88 solar mass and i less than 61 deg (95% confidence lower and upper limit, respectively), thereby making Cyg X-2 the highest mass neutron star measured to date. If confirmed this would set significant constraints on the equation of state of nuclear matter.