The theory that states that mitochondria and chloroplasts are derived from free-living prokaryotic cells is called the Endosymbiotic Theory.

Here's a breakdown of the theory:

* Endosymbiosis: This refers to a relationship where one organism lives inside another organism.

* The Theory: The Endosymbiotic Theory proposes that ancient eukaryotic cells engulfed prokaryotic cells, which then evolved into mitochondria (for cellular respiration) and chloroplasts (for photosynthesis).

* Evidence: There's a lot of evidence supporting this theory:

* Similarities in structure: Mitochondria and chloroplasts have their own DNA, ribosomes, and double membranes, similar to prokaryotic cells.

* DNA sequence analysis: The DNA of mitochondria and chloroplasts is more closely related to prokaryotic DNA than eukaryotic DNA.

* Replication: Mitochondria and chloroplasts replicate independently of the eukaryotic cell, similar to how prokaryotes divide.

This theory is widely accepted in the scientific community and is a cornerstone of our understanding of the evolution of eukaryotic cells.