A system for in vivo breast imaging with monochromatic x-rays has been designed and built at the synchrotron radiation facility Elettra in Trieste (Italy) and will be operational in 2004. The system design involves the possibility of performing both planar mammography and breast tomography. In the present work, the first results obtained with a test set-up for breast tomography are shown and discussed. Tomographic images of in vitro breasts were acquired using monochromatic x-ray beams in the energy range 20-28 keV and a linear array silicon pixel detector. Tomograms were reconstructed using standard filtered backprojection algorithms; the effect of different filters was evaluated. The attenuation coefficients of fibroglandular and adipose tissue were measured, and a quantitative comparison of images acquired at different energies was performed by calculating the differential signal-to-noise ratio of fibroglandular details in adipose tissue. All images required a dose comparable to the dose delivered in clinical, conventional mammography and showed a high resolution of the breast structures without the overlapping effects that limit the visibility of the structures in 2D mammography. A quantitative evaluation of the images proves that the image quality at a given dose increases in the considered energy range and for the considered breast sizes.