A color appearance model (CAM) is an advanced colorimetric tool used to predict color appearance under a wide variety of viewing conditions. A chromatic adaptation transform (CAT) is an integral part of a CAM. Its role is to predict "corresponding colors," that is, a pair of colors that have the same color appearance when viewed under different illuminants, after partial or full adaptation to each illuminant. Modern CATs can sometimes generate colors with negative tristimulus values. For some imaging applications, it is important to maintain positive tristimulus values when applying a CAT. This article proposes a new CAT that does not operate on the standard von Kries model of adaptation. Instead, it uses a spectral reconstruction technique as an intermediate stage in the process, while still requiring only tristimulus values as inputs. It is demonstrated that the proposed CAT will not generate colors outside the spectral locus or colors with negative tristimulus values. The proposed CAT does not use established empirical corresponding-colors data sets to optimize performance, as most modern CATs do, yet it performs as well as or better than the most recent CATs when tested against the data sets of corresponding colors.