We exploit the quantum coherence between pair-produced D0 and D[over]0 in psi(3770) decays to study charm mixing, which is characterized by the parameters x and y, and to make a first determination of the relative strong phase delta between D0-->K+pi- and D[over]0-->K+pi-. Using 281 pb(-1) of e+e- collision data collected with the CLEO-c detector at Ecm=3.77 GeV, as well as branching fraction input and time-integrated measurements of RM identical with (x2 + y2)/2 and RWS identical with Gamma(D0-->K+pi-)/Gamma(D[over]0-->K+pi-) from other experiments, we find cosdelta=1.03(-0.17)(+0.31)+/-0.06, where the uncertainties are statistical and systematic, respectively. By further including other mixing parameter measurements, we obtain an alternate measurement of cosdelta=1.10+/-0.35+/-0.07, as well as x sindelta=(4.4(-1.8)(+2.7)+/-2.9)x10(-3) and delta=(22(-12-11)(+11+9)) degrees .