The reaction of magnesium atoms and clusters with oxygen molecules has been investigated in liquid helium droplets at T = 0.37 K. The energy released during the reaction predominantly leads to the ejection of the reaction products out of the He droplets. The product molecules Mg2O, Mg2O2, Mg3O, Mg3O2, and Mg4O2 were detected by mass spectrometry. With more than one Mg atom picked up per He droplet, chemiluminescence (CL) light could be detected. This CL results from electronically and vibrationally excited reaction products (MgnO2, n >= 2) which left the He droplets. For large He droplets with diameter d > 13 nm, the intensity of the CL light decreases linearly with increasing He droplet diameter. No evidence for chemical reaction was found for d > 50 nm. A considerable time delay between chemical reaction and light emission was observed. It was found that the chemical reaction is unexpectedly fast and has a first-order reaction rate larger than 5 x 10(4) s(-1).