The video is purportedly of an event in neighbouring Thane district on June 17.
Chavan cited the example of Abraham Lincoln narrating a story where Lincoln picked up a "piglet" from a drain and cleaned it.
"Similarly, Prime Minister Narendra Modi and Maharashtra Chief Minister Devendra Fadnavis too were working hard to uplift Dalits," Chavan said.
The analogy sparked protest and Thane district unit of NCP organised a "naming ceremony" of a pig and named it 'Ravindra Chavan'.
NCP spokesperson Nawab Malik said the BJP MLA should tender an apology for the "appalling analogy".