To　enhance　the　strength　of　chiral　light–matter　interaction　for　practical　applications,　the　chirality　and　quality　factors　(Q-factors)　of　current　methods　need　to　be　strengthened　simultaneously.　Here,　we　propose　a　design　of　photonic　crystal　slabs　(PhCs)　supporting　chiral　bound　states　in　the　continuum　(BICs)　of　transverse　electric　(TE)　and　transverse　magnetic　(TM)　modes,　exhibiting　maximal　chiroptical　responses　with　high　Q-factors　and　near-unity　circular　dichroism　(CD　=　0.98).　Different　from　the　past,　the　PhCs　we　employed　only　have　reduced　in-plane　symmetry　and　can　support　simultaneously　chiral　quasi-BICs　(q-BICs)　of　TE　and　TM　mode　with　two-dimensional　ultra-strong　external　and　internal　chirality.　Based　on　the　temporal　coupled-mode　theory,　two　analytical　expressions　of　CD　of　chiral　q-BICs　response　are　revealed,　which　are　consistent　with　the　simulation　results.　Furthermore,　we　elucidate　these　results　within　the　charge-current　multipole　expansion　framework　and　demonstrate　that　the　co-excitation　of　higher-order　multipole　electric/magnetic　modes　is　responsible　for　near-perfect　CD.　Our　results　may　provide　more　flexible　opportunities　for　various　applications　requiring　high　Q-factors　and　chirality　control,　such　as　chiral　lasing,　chiral　sensing,　and　enantiomer　separation.　©　2023　Chinese　Laser　Press.