Yes, you can. If you say 'I've got a frozen chicken' it means that you have one whole bird - hence the singular/countable noun. If you say 'I've got frozen chicken', this simply means that you have some of this type of meat in your freezer which is frozen. It could be several birds, or various different chicken pieces, or slices of chicken - we don't know.

Thank a lot Bramwell! Your explanation was very helpful!

You can say 'I've got a chicken' if you have one whole bird, alive or as meat. The difference between chicken and most other types of meat is twofold, firstly most meats have a different name from the live animal, secondly it would be very unusual to have a whole pig or cow unless the person was a farmer.