A chemical reactor including: a plurality of heat exchange plates which between them define reaction compartments, in which reactor each heat exchange plate includes two walls between them defining at least one heat exchange space, the respective walls being fixed together by joining regions, and the reactor also comprises at least one injection device for injecting substance into the reaction compartments, said substance-injection device passing through the heat-exchange plates in respective joining regions thereof. Also, a chemical reaction process that can be carried out in this reactor.