Glycolysis is known to be a part of cellular metabolism undergone by both eukaryotic and prokaryotic cells, whether under aerobic or anaerobic conditions. As the endosymbiotic theory states that mitochondria and chloroplasts were once bacteria that lived apart from eukaryotic cells, do they have any enzymes or compounds suggesting that they once did glycolysis?
A search of UniProt returns no reviewed, mitochondrially encoded genes involved in glycolysis. There are some unreviewed entries, but a brief perusal of the associated publications suggests to me that these have all been incorrectly annotated (as one may expect from unreviewed entries).
Interestingly, Rickettsia prowazekii, an obligate intracellular parasite and the modern species thought to be most closely related to mitochondria, also has no glycolytic enzymes:
Genome sequences of organisms enjoying an endosymbiotic lifestyle are at risk. The activities of homologous nuclear genes may render genes of the endosymbiont expendable and as a consequence they become vulnerable to obliteration by mutation. Good candidates for such purged genes in Rickettsia and mitochondria are genes required for amino-acid biosynthesis, nucleoside biosynthesis and anaerobic glycolyis. These and other genes would have been deleted when an ancestral genome first lived in a nucleated cell. Once genes essential to a free-living mode are lost, the endosymbiont becomes an obligate resident of its host.
Andersson SGE, Zomorodipour A, Andersson JO, Sicheritz-Pontén T, Alsmark UCM, Podowski RM, Näslund AK, Eriksson A-S, Winkler HH, Kurland CG. 1998. The genome sequence of Rickettsia prowazekii and the origin of mitochondria. Nature 396:133-140.