Step 1: Understanding the Concept
A biopatent is a patent granted for a living organism or a biological invention.
Step 2: The first biopatent
In 1980 the USA granted a patent to Ananda Mohan Chakrabarty for a Pseudomonas bacterium engineered to break down crude oil, useful for cleaning oil spills.
Step 3: Other options
Patents on genes such as the human insulin gene or Bt cotton gene came later.
Final Answer:
The first biopatent was for the oil clearing Pseudomonas bacterium.
\[ \boxed{\text{(C) }\text{Oil clearing ``\textit{Pseudomonas}'' bacterium}} \]