The Chase is the eighth serial of the second season of the British science fiction television series Doctor Who. Written by Terry Nation and directed by Richard Martin, the serial was broadcast on BBC in six weekly parts from 22 May to 26 June 1965. Set in multiple time periods on several different planets, including Aridius, Earth, and Mechanus, the serial features the Dalek race travelling through time while pursuing the TARDIS and its occupants—the First Doctor (William Hartnell) and his companions Ian Chesterton (William Russell), Barbara Wright (Jacqueline Hill), and Vicki (Maureen O'Brien)—to kill them and seize the TARDIS for themselves. The Doctor and companions encounter several characters, including monsters Dracula (Malcolm Rogers) and Frankenstein's monster (John Maxim), human astronaut Steven Taylor (Peter Purves), and an android replica of the Doctor (Edmund Warwick).

Nation was commissioned to write the serial by story editor Dennis Spooner following the success of the Daleks in The Daleks (1963–1964) and its sequel The Dalek Invasion of Earth (1964); Martin was also chosen to direct based on his work on these serials. The Chase was the final work on Doctor Who by Martin as director and Spooner as script editor. The story was allocated a larger budget than normal, resulting in minimal budget for the preceding and following stories. A substantial part of the budget was allocated to the construction of the Mechonoids; they were given a press launch, and their merchandising rights were offered to manufacturers. The production crew coordinated with the Beatles's manager Brian Epstein to feature a clip of the band in the first episode of The Chase. Dudley Simpson composed the serial's incidental score.

The serial marks the final appearance of series regulars Russell and Hill, who depart in the sixth episode; their decisions, made independently, greatly upset Hartnell. It marks the first appearance of Purves, whose appearance in the third episode as Morton Dill led to his casting in the sixth as Steven Taylor, who later became a companion. Warwick worked with Hartnell to imitate his mannerisms as the android replica of the Doctor. Due to the variety of work, set designers Raymond Cusick and John Wood collaborated for the serial; Cusick redesigned some Daleks that had been modified since their original creation. The production crew sourced Dalek props that were on loan to various studios and companies, including for the film Dr. Who and the Daleks (1965). Filming for the serial took place at Riverside Studios from April to June 1965.

The Chase received high viewership, ranging from nine to ten million viewers, and successful Appreciation Index scores, though both were lower than the previous Dalek serial, The Dalek Invasion of Earth. Contemporary reviews improved as broadcast continued; the early episodes were found to be confusing and lacklustre, with the Daleks losing their appeal, though later episodes were praised for the battle between the Daleks and Mechonoids, the cast's performances, and the departure of Ian and Barbara. Retrospective reviews were mixed, with similar praise for the Mechonoids and characters, and criticism towards the comedy and unbelievability of some scenes and concepts. The story was novelised and released on VHS, DVD, Blu-ray, and as an audiobook, with music and sound effects released on CD.

While Ian Chesterton and Vicki explore the Sagarro Desert on the planet Aridius, the First Doctor and Barbara Wright remain in the TARDIS. They see the Daleks embarking on a plan to follow the TARDIS to Aridius to exterminate the Doctor and his companions and seize his ship. Realising these events happened in the past and the Daleks may already be on Aridius, the Doctor and Barbara venture out to warn Ian and Vicki, only to see Daleks emerging from the sands after a dust storm. The Doctor and Barbara are saved by native Aridians and reunited with Vicki and Ian, who were injured after an encounter with Mire Beasts. The Beasts attack and, in the confusion, the Doctor and his friends flee to the TARDIS.

The Daleks pursue the TARDIS through time and space in their own vessel. The Doctor and companions stop atop the Empire State Building in New York City in 1966; after they leave, a Dalek appears. They are later mistaken for stowaways on the Mary Celeste until Daleks arrive and the frightened boat crew abandon the ship. In a mysterious old house, the Doctor and his companions encounter Dracula and Frankenstein's monster, who attack the pursuing Daleks. In the confusion, the group leave Vicki behind, unaware the monsters were actually robots in a defunct futuristic theme park attraction. Vicki stows away aboard the Dalek ship and witnesses them create an android replica of the Doctor, which is dispatched on Mechanus. Vicki reunites with the Doctor, Ian, and Barbara, but a fight ensues between Ian and the real Doctor once the robot duplicate appears, claiming to be the original. When the robot Doctor mistakenly refers to Vicki as his granddaughter Susan, Barbara realises and the real Doctor disables the robot.

As the Doctor and his companions venture into a metal city above the jungle, Mechonoids imprison them with shipwrecked human astronaut Steven Taylor. Under the cover of the Daleks' attack on the city, the Doctor and his companions escape. Upon discovering the Dalek time machine and considering it more reliable than the TARDIS, Ian and Barbara persuade the Doctor to help them operate it to return to London in their own time. Upon arriving in London, 1965, Ian and Barbara set the time machine to auto-destruct. The Doctor says that he will miss Ian and Barbara, and he and Vicki depart in the TARDIS.

Following the success of the Daleks in their introductory serial The Daleks (1963–1964) and its sequel The Dalek Invasion of Earth (1964), writer Terry Nation was quickly commissioned to write a third serial by new story editor Dennis Spooner, with whom he was old friends due to their history of comedy writing. Nation's original story pitch was scrapped for unknown reasons, and he was instead commissioned to write a six-episode Dalek serial, tentatively titled Doctor Who and the Daleks (III), around mid-December 1964. Nation submitted a five-page synopsis on 10 January 1965 to producer Verity Lambert, aware of the fact that it would be a more expensive production than typical. In Nation's synopsis, the story was known as Dr Who (Segment: Dalek Three) – The Pursuers; a few months later, it became The Chase. Nation wrote the scripts between writing episodes of The Saint (1962–1969). In the first episode's script, Nation suggested the footage of the Gettysburg Address could be borrowed from the 1962 film How the West Was Won. Nation's scripts required little editing from Spooner, though he was too busy to undertake rewrites regardless.