The number of indirectly detected planetary systems around nearby stars has grown tremendously since their initial discovery five years ago. But the direct observation of light reflected from these systems remains a formidable task, because of the high contrast ratios between them and their parent stars, and because of the tiny angular separations. Theoretically, these difficulties can be overcome by using a dual-aperture stellar interferometer in which the starlight is cancelled, or 'nulled' by broadband destructive interference, leaving the planet's light visible. Although the basic requirement of equal and oppositely directed electric fields is easy to state, an experimental demonstration of deep broadband nulling has been lacking, owing to difficulties engendered by the needs for extreme symmetry and stability, and low dispersion in the optical system. Here we report the deep (10(-4)) and stable nulling of broadband (18% bandwidth) thermal light. These results validate the physical principles underlying future planet-searching interferometers, and our laboratory instrument will serve as a prototype for the nulling instrument to be implemented on the Keck interferometer in 2001.