Atoms are usually thought of as achiral objects. However, one can construct superpositions of atomic states that are chiral [1]. Here, we show how to excite such superpositions with tailored light fields both in the weak-field and strong-field regimes, using realistic laser parameters. First, we use time-dependent Schrödinger equation simulations to demonstrate the creation of a time-dependent bound chiral wave packet in sodium atoms. Second, we show how the time-dependent handedness of this wave packet can be probed by photoelectron circular dichroism, in spite of the central symmetry of the core potential. Third, we use time-dependent Schrödinger equation simulations to show how chirality can be directly imprinted on a photoelectron wave packet created by strong-field ionization and introduce an unambiguous chiral measure that allows us to characterize its handedness.