The gravitational wave signal from a binary neutron star inspiral contains information on the nuclear equation of state . This information is contained in a combination of the tidal polarizability parameters of the two neutron stars and is clearest in the late inspiral , just before merger . We use the recently defined tidal extension of the effective one-body formalism to construct a controlled analytical description of the frequency-domain phasing of neutron star inspirals up to merger . Exploiting this analytical description we find that the tidal polarizability parameters of neutron stars can be measured by the advanced LIGO-Virgo detector network from gravitational wave signals having a reasonable signal-to-noise ratio of \rho = 16 . This measurability result seems to hold for all the nuclear equations of state leading to a maximum mass larger than 1.97 M _ { \odot } . We also propose a promising new way of extracting information on the nuclear equation of state from a coherent analysis of an ensemble of gravitational wave observations of separate binary merger events .