New limits on the cosmic equation of state are derived from age measurements of three recently reported old high redshift galaxies ( OHRG ) . The results are based on a flat FRW type cosmological model driven by nonrelativistic matter plus a smooth component parametrized by its equation of state p _ { x } = \omega \rho _ { x } ( \omega \geq - 1 ) . The range of \omega is strongly dependent on the matter density parameter . For \Omega _ { M } \sim 0.3 , as indicated from dynamical measurements , the age estimates of the OHRG restricts the cosmic parameter to \omega \leq - 0.27 . However , if \Omega _ { M } is the one suggested by some studies of field galaxies , i.e , \Omega _ { M } \simeq 0.5 , only a cosmological constant ( \omega = -1 ) may be compatible with these data .