D

Step 1: Identifying the experiment: The integral multiples of the elementary charge were demonstrated by Robert Millikan in his famous oil drop experiment.
Step 2: Understanding the oil drop experiment: In this experiment, Millikan observed tiny oil droplets that were electrically charged, and he was able to measure the charge on these droplets as they fell under the influence of gravity and electric fields.
Step 3: Results of the experiment: Millikan concluded that the measured charges were always integral multiples of a smallest charge value, which is the charge of a single electron (approximately \(1.6 \times 10^{-19} C\)). This provided strong evidence for the quantization of electric charge.
Therefore, the correct answer is D: Millikan.