Step 1: An HIV patient with chronic watery diarrhea is the classic setting for an opportunistic protozoal gut infection.
Step 2: The biopsy shows small (2 to 5 \(\mu\)m) basophilic round bodies sitting along the apical brush border of the enterocytes, appearing to protrude from the cell surface (the so-called blue beads), within the cell membrane. This intracellular but extracytoplasmic location is characteristic of Cryptosporidium.
Step 3: Supporting features are villous atrophy, crypt hyperplasia and a mixed inflammatory infiltrate in the lamina propria. The organisms highlight with Giemsa. CMV would show large cells with intranuclear owl-eye inclusions, Giardia shows pear-shaped trophozoites in the lumen, and microsporidia are tiny spores best seen on special stains, none matching the apical bead appearance.
Answer: Cryptosporidium.
Ref: Mandell, Douglas, and Bennett's Principles and Practice of Infectious Diseases, 8e.