Final answer:
The mitochondria are the organelles in eukaryotic cells that produce large quantities of ATP, using the chemical energy from glucose in the presence of oxygen.
Step-by-step explanation:
The organelle responsible for producing large quantities of ATP when both glucose and oxygen are available to the eukaryotic cell is the mitochondria. These are referred to as the "powerhouses" or "energy factories" of the cell. The mitochondria carry out cellular respiration where they convert the chemical energy found in glucose into ATP, which is the main energy carrier molecule within the cell. This process requires oxygen and results in the production of carbon dioxide as a waste product, which is subsequently exhaled during breathing.