**Core Concept**
The question pertains to the historical milestone of liver transplantation, highlighting the pioneering work in the field of organ transplantation. The liver is a vital organ responsible for detoxification, protein synthesis, and production of biochemicals necessary for digestion.

**Why the Correct Answer is Right**
The first successful liver transplant was performed by Dr. Thomas Starzl in 1963 at the University of Colorado. This groundbreaking surgery marked a significant milestone in the development of organ transplantation. The recipient, a 3-year-old boy, received a liver from his twin brother. The success of this procedure paved the way for further advancements in liver transplantation and other organ transplants.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because the first liver transplant was not performed in the United States by Dr. David Hume.
**Option B:** Incorrect because the first liver transplant was not performed in the United Kingdom by Sir Peter Medawar.
**Option C:** Incorrect because the first liver transplant was not performed in Australia by Dr. Barry Doyle.

**Clinical Pearl / High-Yield Fact**
The pioneering work of Dr. Thomas Starzl in liver transplantation led to significant improvements in immunosuppressive therapy, making organ transplantation a viable treatment option for patients with end-stage liver disease.

**Correct Answer: C. The University of Colorado.**