Fire crews received an emergency call from a home in Vicarage Street, near Erskine Road park, at around 3.10am on Wednesday, June 24.
Three people were found trapped inside one of the upstairs rooms when firefighters arrived, with flames were tearing through the bottom floor of the building.
The terrified family were rescued by firefighters who smashed through an upstairs window before being handed over to paramedics at the scene.
Sean Fisher, 24, is now wanted by police in connection with an arson investigation.
A spokesman for Lancashire Police said: "Fisher, 24, of no fixed abode, is wanted after a fire at a property on Vicarage Street, Chorley on June 24."
Fisher is described as white and of medium build.
He has links to the Chorley area.
Anybody with information can contact police by calling 101 or emailing [email protected] In an emergency call 999.
Alternatively, independent charity Crimestoppers can be contacted anonymously on 0800 555111 or online at https://crimestoppers-uk.org/