We present kinematical evidence that the irregular galaxy located 26'' northwest of IZw18 -the most metal-poor blue-compact-dwarf (BCD) galaxy known- is a dynamically associated companion system. Longslit CCD spectra were obtained in 1996 February using the 4.2m WHT+ISIS at La Palma, with the slit placed across the NW HII region of IZw18 and through an Hα knot in the center of the companion galaxy. Deep CCD spectra were acquired simultaneously in the blue and red spectral regions; with the blue covering Hβ and [OIII] 4959,5007 Angstroms, and the red covering Hα . The red spectra showed continuous Hα emission from the BCD main body of IZw18 to the Hα knot in the companion galaxy. The heliocentric radial velocity variation for the Hα line across a 50'' length of slit ( ~ 2.4 kpc for a distance of 10 Mpc for IZw18) shows a smooth double-sinusoidal variation ranging from +730 km/s just NW of the brightest star-forming region in IZw18 to +780 km/s in the SE extremity of the main body. The heliocentric velocity of the brightest Hα knot in the main body was measured as +741.0+/-0.1 km/s and that of the Hα knot in the companion was found to be +752+/-2 km/s (where the errors are the residuals of the gaussian fits; systematic errors are yet to be evaluated). In addition to the radial velocity information, we present an analysis of high velocity gas seen in the wings of Hα and other lines at several locations across IZw18 and in the Hα knot of the companion system (where we find the knot to be an expanding cloud, with vexp ~ 100 km/s). Previous HST WFPC2 imagery (Dufour et al. 1995, BAAS, 27, 86) indicated that the companion system (``C'') was a dwarf irregular galaxy of type Im that resolved into stars at the V~24.5 level. They also noted that it contained stars as young as ~ 40 Myr -if it were at the same distance as IZw18. Our new results prove that ``IZw18'' consists of a pair of dwarf irregulars, one currently undergoing a starburst (the BCD namesake) and another nearby ( ~ 1.5 kpc in the plane of the sky) Im system which has had an older star formation history.