Measures of exoplanet bulk densities indicate that small exoplanets with radius less than 3 Earth radii (R⊕) range from low-density sub-Neptunes containing volatile elements1 to higher-density rocky planets with Earth-like2 or iron-rich3 (Mercury-like) compositions. Such astonishing diversity in observed small exoplanet compositions may be the product of different initial conditions of the planet-formation process or different evolutionary paths that altered the planetary properties after formation4. Planet evolution may be especially affected by either photoevaporative mass loss induced by high stellar X-ray and extreme ultraviolet (XUV) flux5 or giant impacts6. Although there is some evidence for the former7,8, there are no unambiguous findings so far about the occurrence of giant impacts in an exoplanet system. Here, we characterize the two innermost planets of the compact and near-resonant system Kepler-107 (ref. 9). We show that they have nearly identical radii (about 1.5-1.6R⊕), but the outer planet Kepler-107 c is more than twice as dense (about 12.6 g cm-3) as the innermost Kepler-107 b (about 5.3 g cm-3). In consequence, Kepler-107 c must have a larger iron core fraction than Kepler-107 b. This imbalance cannot be explained by the stellar XUV irradiation, which would conversely make the more-irradiated and less-massive planet Kepler-107 b denser than Kepler-107 c. Instead, the dissimilar densities are consistent with a giant impact event on Kepler-107 c that would have stripped off part of its silicate mantle. This hypothesis is supported by theoretical predictions from collisional mantle stripping10, which match the mass and radius of Kepler-107 c.