Dispersive mirrors operating in a broadband infrared spectral range are reported for the first time. The mirrors are based on Si/SiO2 thin-film materials. The coatings exhibit reflectance exceeding 99.6% in the spectral range from 2 to 3.2 µm and provide a group delay dispersion of -100 fs2 and -200 fs2 in this range. The fabricated mirrors are expected to be key elements of Cr:ZnS/Cr:ZnSe femtosecond lasers and amplifiers. The mirrors open a new avenue in the development of ultrafast dispersive optics operating in the infrared spectral range.