If you are offering someone chicken, you can say either 'Would you like some chicken?' or 'Would you like any chicken?'. The meaning and the function is the same. In both cases, the chicken exists! It's probably sitting on a serving dish in the middle of the table. There is a subtle difference, though. 'Would you like some ...?' is neutral. It's an offer which you think has a good chance of being accepted 'Would you like any...?' is based on an assumption that they person may not want any chicken. You might say that if you know that the person is quite full because they have already eaten plenty of other food, or because they had already told you that they would probably just have some salad. Or maybe the chicken was burnt and unappetising, and so you're not expecting anyone to want any. Whatever the reason, when you make an offer with '...any chicken?', you have the idea of 'no chicken' in your mind.

Yes, there is a difference. "Any chicken" means either that the chicken does not exist or it is not known if the chicken exists. For example, in a grocery store: - A customer: "Do you have any chicken?" (The customer does not know if the chicken exists.) - The butcher: "No, we do not have any chicken." (The chicken does not exist.) "Some chicken" means that the chicken is known to exist (or one assumes it exists) and a portion of the existing chicken is under discussion. - A customer: "Do you have any chicken?" (The customer does not know if any chicken exists.) - The butcher: "Yes, we have chicken. Would you like some chicken?" (The existence has been confirmed. The butcher is asking about a portion of it.) - The customer: (looking in his grocery cart): "I don't have any chicken yet." (There is no chicken in the grocery cart.) - The customer: "Yes, I would like some chicken." (The customer wants a portion of the chicken that is known to exist with the butcher.) Another example: - The child: "Is there any cake?" (The cake may or may not exist.) - The mother: "Yes. Do you want some cake?" (The cake does exist. Now, a portion of the cake is under discussion.) - The child: "Yes, with some ice cream." (The child assumes there is ice cream and wants a portion of the assumed ice cream.) - The mother: "But we don't have any ice cream." (The mother corrects the child, identifying the ice cream does not exist.) - The child: "Oh. Well, I still want some cake." (The cake still exists, and the child still wants a portion of the cake.)

Even though many native speakers use these interchangeably, it's best to say, Would you like some chicken? because the question is affirmative. ANY would be used in more negative connotations, -I don't want any chicken.-