We performed angle-resolved photoemission (ARPES) experiments with circularly polarized light and first-principles density functional calculation with spin-orbit coupling to study surface states of a topological insulator . We observed circular dichroism (CD) as large as 30% in the ARPES data with upper and lower Dirac cones showing opposite signs in CD. The observed CD is attributed to the existence of local orbital-angular momentum (OAM). First-principles calculation shows that OAM in the surface states is significant and is locked to the electron momentum in the opposite direction to the spin, forming chiral OAM states. Our finding opens a new possibility for strong light-induced spin-polarized current in surface states. We also provide a proof for local OAM origin of the CD in ARPES.