  We exploit the quantum coherence between pair-produced D0 and D0bar 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 D0bar -> K+pi-. Using 281 pb^-1 of e^+e^-
collision data collected with the CLEO-c detector at E_cm = 3.77 GeV, as well
as branching fraction input and time-integrated measurements of R_M =
(x^2+y^2)/2 and R_{WS} = Gamma(D0 -> K+pi-)/Gamma(D0bar -> K+pi-) from other
experiments, we find \cos\delta = 1.03 +0.31-0.17 +- 0.06, where the
uncertainties are statistical and systematic, respectively. By further
including other mixing parameter measurements, we obtain an alternate
measurement of \cos\delta = 1.10 +- 0.35 +- 0.07, as well as x\sin\delta = (4.4
+2.7-1.8 +- 2.9) x 10^-3 and \delta = 22 +11-12 +9-11 degrees.
