The process described in this invention is able to use most forms of organic waste as feedstock, although waste with high sugar, starch, and/or protein content is preferred. The waste material is prepared for fermentation by grinding it to a particle size of < 1 mm and adjusting its pH to 5.5. Subsequently, the prepared waste material is anaerobically digested by a multi-species consortium of microbes comprising both bacteria and archaea members. Undesirable production of side products is a major challenge faced in obtaining high yields of lactic acid. The Inventors describe a pH-based technique to simultaneously limit production of methane and short-chain fatty acids, which are the primary side products competing with lactic acid. By using a microbial community instead of a monoculture and by using pH to control the composition of fermentation products, this invention allows production of lactic acid from organic waste while avoiding the significant overheads associated with feedstock sterilization or the use of antibiotics or other specialty chemicals to control yield. The Inventors have achieved lactic acid yields of over 100 g per ton of organic food waste using this process.