Under the Axiom of Determinacy, the least uncountable cardinal omega_1 behaves like a large cardinal. We will present a theorem due to Woodin saying that from a strong form of determinacy, namely AD_R + "Theta is regular," one can force the Axiom of Choice together with the statement "there is an omega_1-dense ideal on omega_1." In essence, omega_1 retains a trace of its "large cardinal" nature that is consistent with AC.