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 serial marks the final appearance of series regulars Russell and Hill, who depart in the sixth episode; their decisions, made independently, greatly upset Hartnell.

Subsequently, landing in a mysterious old house, the Doctor and his companions encounter Dracula (Malcolm Rogers) and Frankenstein's monster (John Maxim), who attack the pursuing Daleks.

Vicki stows away aboard the Dalek ship and witnesses them create an android replica of the Doctor (Edmund Warwick), programmed to kill the TARDIS crew, which is dispatched on arrival on the hostile jungle world of Mechanus.

As the Doctor and his companions venture into a metal city above the jungle, Mechonoids imprison them with shipwrecked human astronaut Steven Taylor (Peter Purves).

[16] An external model sequence of the haunted house in the fourth episode was cut from the script when the reasoning behind the sequence—taking place in a futuristic theme park attraction as opposed to inside the minds of its occupants—was changed.

[13] A substantial part of the serial's budget was allocated to the construction of the Mechonoids,[18] with a total cost of £812;[19] they were given a press launch on 14 April 1965,[20] and their merchandising rights were offered to manufacturers.

[18] An early intention was for the first episode to feature the Beatles, dressed as old men, performing in the studio as part of a fictional 50th anniversary concert; the idea was rejected by the band's manager, Brian Epstein, who thought it would be poor for the group's image.

[18] The production team enquired about obtaining material of the Beatles from Top of the Pops, but discovered that most episodes had been wiped after broadcasting; they were offered a November 1964 recording of "I Feel Fine" at Riverside Studio.

[21] This had the unintended effect of making the first episode of The Chase the only remaining source of any surviving Beatles footage from Top of the Pops, as much of the show was wiped.

[20] Cusick also designed a lightweight prop, referred to as a "hover Dalek", which could appear to move rapidly over the sands; it was operated by Gerald Taylor.

[40] Lambert was unsatisfied with the set of the Empire State Building; she complained to the design department's Barry Learoyd on 26 May, and wrote "even bearing in mind the necessary economy because of the budget, this is pretty poor by any standards".

[28] Following the recording of the last episode, Martin wrote to Cusick and Wood to thank them for their work on the serial, crediting them for significantly contributing to any praise that the story would receive.

[44] The Chase marks the final appearance of series regulars William Russell and Jacqueline Hill as Ian Chesterton and Barbara Wright, respectively.

Their departure was announced on 1 April 1965; Russell explained the creativity had gone and he wanted to reenter comedy and theatre performances, and Hill said "It has been great fun, but you can't go on forever".

[47] Edmund Warwick, who portrayed the robotic version of the Doctor, said his scenes were a "thank you" written in for him; the previous year, he had replaced Hartnell at short notice after he was injured during the recording of The Dalek Invasion of Earth.

[49] Arne Gordon, who played the tour guide[a] in the third episode, required special dispensation from the Ministry of Labour and National Service to appear in the show.

[39] In the draft script, Morton was described as a "rather gawky young man... cast in the Hollywood mould of the southern hayseed come to the big city".

[53] After Purves's performance as Morton, Martin, Hartnell, and O'Brien told Lambert they had enjoyed working with him and recommended he be considered to play the next companion.

On 9 April, Martin and a film unit travelled to Camber Sands; to avoid interrupting rehearsals for The Space Museum, David Newman and Barbara Joss stood in for Russell and O'Brien, respectively, with the main actors overdubbing their dialogue later.

[7][19] Locations for the photographs included the Houses of Parliament, Hyde Park, Trafalgar Square, Westminster Bridge, and White City tube station.

[67] Viewership numbers were considered extremely positive, though the early summer months meant that it failed to gain the high audience figures for serials like The Dalek Invasion of Earth and The Web Planet.

After the fourth episode, Philip Purser of the Sunday Telegraph described the show as "a ramshackle old serial these days" and noted the Daleks were "fast losing their ancient menace", criticising their accents.

[69] An audience report prepared on the fourth episode determined the show was "very entertaining" and "refreshingly different from the usual run" of stories, praising the combination of science-fiction and horror and the performances of the regular cast;[70] conversely, some viewers criticised its messy narrative, its frightening scenes for younger audience, and the haunted house sequences, with some feeling the show was losing its appeal despite the Daleks.

[70][71] After the final episode, The Observer's Maurice Richardson praised Hartnell's performance—"no wonder it was so difficult to tell which was the real Who and which the anti-Who robot"—and noted the television show overrode his interest in watching the film Dr. Who and the Daleks.

In The Discontinuity Guide (1995), Paul Cornell, Martin Day, and Keith Topping described the serial as "one of the most bizarre Doctor Who stories" consisting of "unconnected set pieces with only the barest remnant of a plot".

[75] In A Critical History of Doctor Who (1999), John Kenneth Muir similarly considered the serial weaker than its predecessors, with some "droll" and "pointless dead ends", though praised the final battle and farewell sequence.

[80] Total Sci-Fi Online's Jonathan Wilkins likened the serial to pop art and felt "only an utter grouch could dislike a Doctor Who story as zany and iconic as The Chase"; he highlighted the character work concerning Ian and Barbara and the "sense of epic science fiction that is only slightly betrayed by the ever-present problems of budget".

[81] In 2012, SFX's Steve O'Brien named the haunted house sequence and the android Doctor among the "silliest moments" in the show's history,[82] though Will Salmon considered Ian and Barbara's departure as among the best of any companion;[83] Den of Geek's Andrew Blair echoed the latter sentiment in 2021.

The serial was released in a DVD box set alongside the preceding serial, The Space Museum, in March 2010; it features an audio commentary with Russell, O'Brien, Martin, and Purves, as well as documentaries about the production, the characters of Ian and Barbara, the appeal of the Daleks and their merchandising, a history of Shawcraft Models, and Cusick's visit to the art department of Doctor Who after the fourth revived series.