Many chirality-sensitive light–matter interactions are governed by chiral electron dynamics. Therefore, the development of advanced technologies making use of chiral phenomena would critically benefit from measuring and controlling chiral electron dynamics on their natural attosecond timescales. Such endeavours have so far been hampered by the lack of characterized circularly polarized attosecond pulses, an obstacle that has recently been overcome1,2. Here we introduce chiroptical spectroscopy with attosecond pulses and demonstrate attosecond coherent control over photoelectron circular dichroism (PECD)3,4, as well as the measurement of chiral asymmetries in the forward–backward and angle-resolved photoionization delays of chiral molecules. We show that co-rotating attosecond and near-infrared (IR) pulses can nearly double the PECD and even change its sign compared with single-photon ionization. We demonstrate that chiral photoionization delays depend on both polar and azimuthal angles of photoemission in the light-propagation frame, requiring 3D momentum resolution. We measure forward–backward chiral-sensitive delays of up to 60 as and polar-angle-resolved photoionization delays of up to 240 as, which include an asymmetry of about 60 as originating from chirality in the continuum–continuum transitions. Attosecond chiroptical spectroscopy opens the door to quantitatively understanding and controlling the dynamics of chiral molecules on the electronic timescale.