With the endosymbiotic hypothesis in mind, what structure within modern-day chloroplasts is likely derived from the cytoplasm of an ancestral cyanobacterium that took up residence within a eukaryotic cell?

The chloroplasts had inner membrane

Explanation:

The primitive photoautotrophs utilized hydrogen sulphide as the electron donor to perform photosynthesis for energy production.  

Later upon understanding the endosymbiotic relationship of cyanobacteria which resided in the mitochondria of a eukaryotic host cell, the use of chloroplasts for photosynthesis was understood.  

Generations after generations led to the development of chloroplasts by the cyanobacteria due to this symbiotic relationships which developed into the chloroplasts.

The unique presence of the inner membrane and its components like the stroma, thyllakoids helped the organism to utilize water as the electron donor for photosynthesis like the present day eukaryotes. This is the main reason why cyanobacteria is considered as the ancestor for eukaryotes.