Step 1: Understanding the Concept:
Frederick Sanger's dideoxy chain-termination sequencing method achieved the first complete nucleotide sequence of an entire organismal DNA genome in 1977.
Key Formula or Approach:
\[ \text{Bacteriophage } \phi\text{X174 Genome} = 5,386\text{ nucleotides (Circular Single-Stranded DNA)} \]
Step 2: Detailed Explanation:
Genomic sequencing milestones:
1. Bacteriophage $\phi$X174 (1977): Frederick Sanger and colleagues at the MRC Laboratory of Molecular Biology determined the complete 5,386-nucleotide genome of bacteriophage $\phi$X174 using the dideoxy chain termination method, representing the first complete DNA genome ever sequenced in biological history.
2. Bacteriophage $\lambda$ ($48.5\text{ kb}$) was sequenced in 1982.
3. Haemophilus influenzae was the first free-living cellular organism sequenced in 1995.
Step 3: Final Answer:
Hence, the full DNA genome was first completely sequenced in Bacteriophage phiX174, corresponding to option (A).