H(35)Cl(v=0,J=0) molecules in a supersonic expansion were excited to the H(35)Cl(v=2,J=1,M=0) state with linearly polarized laser pulses at about 1.7 microm. These rotationally aligned J=1 molecules were then selectively photodissociated with a linearly polarized laser pulse at 220 nm after a time delay, and the velocity-dependent alignment of the (35)Cl((2)P(32)) photofragments was measured using 2+1 REMPI and time-of-flight mass spectrometry. The (35)Cl((2)P(32)) atoms are aligned by two mechanisms: (1) the time-dependent transfer of rotational polarization of the H(35)Cl(v=2,J=1,M=0) molecule to the (35)Cl((2)P(32)) nuclear spin [which is conserved during the photodissociation and thus contributes to the total (35)Cl((2)P(32)) photofragment atomic polarization] and (2) the alignment of the (35)Cl((2)P(32)) electronic polarization resulting from the photoexcitation and dissociation process. The total alignment of the (35)Cl((2)P(32)) photofragments from these two mechanisms was found to vary as a function of time delay between the excitation and the photolysis laser pulses, in agreement with theoretical predictions. We show that the alignment of the ground-state (35)Cl((2)P(32)) atoms, with respect to the photodissociation recoil direction, can be controlled optically. Potential applications include the study of alignment-dependent collision effects.