In English, the phrase "I have chicken" can only be plural if you're referring to the fact that you possess 'some' chicken, normally cooked. For example, at a restaurant you might be offered 'A plate of chicken' and it could be multiple chickens, but referring to the live animal the plural is always 'Chickens'.
Chickens used for food (pollo in Italian, versus gallo/gallina as a non-food chicken) are (in English) referred to in the singular form, chicken, even when more chicken are meant. So translating '(multiple edible) polli', would be 'chicken'. Multiple non-edible would be 'galli/galline' in Italian and 'chickens' in English.
I've made a report of the software not seeing 'chicken' as a correct answer.
All the words you mentioned refer to 'masses', eg some water, some sugar, some chicken (as in the meat). Because "polli' is plural, this sentence is refering to some specific chickens (animals), which seems to be why you need the article. That's how I understand it, but I don't know if it's right...