Final answer:
Staphylococcus aureus is the likely causative organism for the rapid onset of vomiting and watery diarrhea after eating a chicken sandwich, with no leukocytes or cysts found in the stool examination.
Step-by-step explanation:
In the presented case, a 35-year-old woman along with her coworkers developed vomiting and watery diarrhea after eating a chicken sandwich, suggesting a possible foodborne illness. The absence of leukocytes or cysts in the stool sample rules out certain bacterial and protozoan infections. Given the rapid onset of symptoms, the likely causative organism is Staphylococcus aureus, which is known to produce enterotoxins causing such symptoms within a few hours of ingestion.