Optical chirality (OC) - one of the fundamental quantities of electromagnetic fields - corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.