A number of planned space interferometry missions, including the Laser Interferometer Space Antenna (LISA) gravitational wave detector, require a laser system with high-frequency stability over long time scales. A 1064 nm wavelength nonplanar ring oscillator (NPRO) laser stabilized to a resonant transition in molecular iodine is suitable for these missions, providing high-frequency stability at an absolute reference frequency. The iodine stabilized laser also offers low sensitivity to temperature and alignment fluctuations and allows frequency tuning. We have evaluated the noise performance of a NPRO laser stabilized to iodine using frequency modulation spectroscopy and have found an Allan standard deviation of 10(-14) over 100 s. Simplified optical configurations and the radiation hardness of the frequency-doubling crystals have also been investigated.