We study the preparation and measurement of superpositions of molecular chiral states with sequences of phase-locked ultrashort laser pulses following the scheme proposed by Cina and Harris [J. Chem. Phys. 100, 2531 (1994)]. The model is a parity-invariant molecule with a handed electronic ground state and a harmonic electronic excited state. We analyze the problem by numerically solving the Schrodinger equation. We find that the process of preparation of the superposition of chiral states works very well, in agreement with the analytic approximate solution of Cina and Harris. The detection part, in terms of a fluorescence interferogram, however, turns out to be more delicate. That is, in order to reproduce the main features in the interferogram that reveal the superposition of the chiral states, very stringent conditions on the involved time scale must be satisfied. The most unrealistic characteristic is that very high vibrational states of the (harmonic) excited electronic states are involved. Nevertheless, the proposal is quite feasible and we discuss that the detection restrictions may be softened.