This paper proposes an approach to verify information flow security of concurrent programs. It discusses a hyperproperty called observational determinism which aims to ensure secure information flow in concurrent programs, and proves how this hyperproperty can be verified by stutter equivalence checking. More precisely, it defines observational determinism in terms of stutter equivalence of all traces having the same low initial value and shows how stutter trace equivalence can be verified by computing a divergence stutter bisimulation quotient. The approach is illustrated by verifying a small example.