Planets with mass similar to Jupiter's are now known to orbit nearby stars. Are there also planets like Earth? If so, their thermal emission should be directly detectable, and thermal spectra could identify the strong features of carbon dioxide, water and ozone at the levels seen in Earth. But the very close angular separation (approximately 0.1 arcsec) and huge brightness difference (approximately 107) between a star and such a planet present a technical challenge. Space interferometry could in principle solve both problems, by using destructive interference to cancel out the stellar emission, and aperture synthesis to recover high angular resolution images. We show how these two functions conflict, and point to a new interferometer design which allows them to be reconciled. One key technical challenge is to combine beams with strictly controlled amplitude and achromatic phase inversions, so as to cancel the stellar disc flux by a factor of a million. We show how refractive elements analogous to an achromatic lens can be used for this purpose.