Okay, let's tackle this question. So, the scenario is a 2-year-old child with fever, vomiting, and neck rigidity. The CSF findings are high WBC count (2000/ml), elevated protein (100 mg/dl), and Gram stain shows Gram-negative bacilli. The culture grows only on chocolate agar, not blood agar. The question is asking for the causative agent.

First, I need to recall the common causes of bacterial meningitis in children. The key here is the Gram stain result and the culture growth. Gram-negative bacilli suggests possibilities like E. coli, H. influenzae, or maybe Pseudomonas. But the culture only grows on chocolate agar. Now, chocolate agar is used for organisms that require extra nutrients, like Haemophilus species. H. influenzae is a Gram-negative coccobacillus and requires X and V factors, hence needs chocolate agar. Blood agar is for other bacteria like Streptococcus pneumoniae.

Wait, but H. influenzae is a coccobacillus, not a bacillus. The question says Gram-negative bacilli. So maybe E. coli? But E. coli would grow on blood agar. Also, E. coli is a Gram-negative bacillus. However, H. influenzae might be a better fit here because of the chocolate agar requirement. Also, in children under 5, H. influenzae type b was a common cause before the vaccine. But since the options aren't given, I need to think about the typical organisms.

Another possibility is Neisseria meningitidis, which is a Gram-negative diplococcus and would grow on chocolate agar. But the question mentions bacilli, so diplococci might not fit. Then there's Listeria monocytogenes, but that's Gram-positive. So the main contenders here are H. influenzae and maybe E. coli. But since the culture only grows on chocolate agar, H. influenzae is more likely. Also, the child is 2 years old, so H. influenzae could be a cause, though the type b vaccine has reduced its prevalence. But in areas with low vaccination coverage, it's still possible. So the answer is Haemophilus influenzae type b.

**Core Concept**
This question tests the identification of bacterial meningitis pathogens based on Gram stain morphology, culture requirements, and clinical presentation. Gram-negative bacilli that grow only on chocolate agar are characteristic of *Haemophilus influenzae*, which requires X and V growth factors present in chocolate agar but not in standard blood agar.

**Why the Correct Answer is Right**
*Haemophilus influenzae* is a Gram-negative coccobacillus (often described as a short bacillus) that causes meningitis, especially in unvaccinated children under 5. It requires chocolate agar (enriched with X and V factors) for growth because it cannot synthesize heme or NAD independently. The clinical findings (fever, neck rigidity, CSF pleocytosis, and Gram-negative morphology) align with bacterial meningitis, and the culture growth pattern confirms this organism.

**Why Each Wrong Option is Incorrect**
**Option A:** *Escherichia coli* (Gram-negative bacillus) grows on both blood and MacConkey agar, not exclusively on chocolate agar.

✓ Correct Answer: B. heamophilus influenzae