Final answer:
The most compelling evidence for the origin of chloroplasts from photosynthetic cyanobacteria becoming symbiotic inside a host cell is the similarities between chloroplast DNA and cyanobacterial DNA.
Step-by-step explanation:
The strongest evidence supporting the suggestion that chloroplasts originated from photosynthetic cyanobacteria becoming symbiotic inside a host cell is that chloroplast DNA shows similarities to cyanobacterial DNA. Scientists have found that the DNA sequences and chromosome structures of chloroplasts are highly related to those of cyanobacteria. This supports the idea that chloroplasts were once free-living cyanobacteria that were engulfed by eukaryotic cells and established an endosymbiotic relationship.