A 9.1-Hour Candidate Orbital Period for X1556-605

V-band photometry of the low-mass X-ray binary X1556-605 obtained in May 1988 is presented in an attempt to determine the orbital period of the system. The source is seen to be variable by up to 0.6 magnitude on a time scale of hours. Combining the data with those obtained one month later by Schmidtke (1990), Fourier techniques and a recently improved version of the standard period-folding analysis are used to find a probable period of 0.3807 + or - 0.0003 day, with a semiamplitude of about 0.1 magnitude. Both methods indicate that the formal significance of this period detection is greater than 99.9 percent. While independent confirmation is advised before accepting this to be the definite orbital period of the system, a period of this length would not be inconsistent with the X-ray properties of X1556-605 and would, in addition, suggest that the mass-donating companion may be beginning to evolve away from the main sequence.