Using the William Herschel Telescope ISIS spectrograph, deep long-slit spectra were obtained of the ionized gas across the blue compact dwarf galaxy I Zw 18 and in an irregular galaxy located 15" to the northwest. Heliocentric radial velocities of H alpha and H beta emission lines were measured over a 50" length spanning the main body of I Zw 18 all the way to a central bright emission knot of the companion galaxy. This emission shows a smoothly varying double-sinusoidal variation in radial velocity over the length of the slit, which corresponds to about 2.5 kpc in the plane of the sky for an adopted distance of 10 Mpc for I Zw 18. Our primary result is that the radial velocity of an H alpha knot near the center of the companion galaxy is the same as the systemic radial velocity of the ionized gas in the center of the main body of I Zw 18. We also observe a smoothly varying velocity field in the ionized gas between, which we interpret to be strong evidence for the two stellar systems' physical closeness to each other.