In The Chase, we see the emergence of the Daleks of the Time War. Equipped with a time machine of their very own, they have begun a hunt across the fourth dimension for their nemesis. The irony is that this beginning for the trajectory of armadas of Dalek ships bearing down on Gallifrey, screaming "exterminate!" and delivering on the threat is that The Chase is rather light-hearted fare.
Flubs are all over the place throughout, with missed lines, visible stage hands and other missteps. The oddest moments are the comic relief from the Daleks themselves. The pepper-pots of death might have a time machine and a means of tracking the Doctor down across eternity, but what they lack is the competence to see it through. One of the Daleks even has trouble doing simple math!
Nevermind the issue that if the Daleks can track the Doctor down anywhere in time, how did they find and fixate on his first incarnation so easily? That, perhaps, we ought to just chalk up to the fact that writers themselves didn't know that he could regenerate. For the Daleks, this interlude happens immediately in the wake of their foiled invasion of Earth, and that's the Doctor they're looking for.
Fresh from the Space Museum, the quartet of the Doctor, Vicki, Ian and Barbara are watching a device they absconded with: a television that can look in with an objective eye on any point in history. After watching such historic personages as Lincoln, Shakespeare and The Beatles, the viewer catches a glimpse of the Daleks preparing to embark on their mission to destroy the Doctor.
The case begins on the desert planet of Aridus, where twin suns have burned up a global ocean, leaving only a race of floundering mermen and the "mire beasts" that live in the sludge of what were once grand underwater cities. This opening act is straightforward enough, as the people are given the ultimatum of handing over the TARDIS crew or being exterminated. The more comedic elements come when the crew arrive atop the Empire State Building, to the slack-jawed guffaws of a tourist from Arkansas (played by Peter Purves, who would later come into the same serial as space pilot Steven Taylor). Next they arrive for a bit of slapstick on the infamous Mary Celeste, and we learn that it was Daleks who caused the ship to become mysteriously abandoned.
The Daleks are closing in on the TARDIS and the Doctor ominously observes that the next time they land may be the last time. However, neither he nor the Daleks contend with where they land. Both ships materialize in the midst of a foreboding Gothic mansion complete with spiderwebs, flashes of lightening and, somehow, Dracula and the Frankenstein Monster! Though leaving Vicki behind and forcing her to stow away on the Dalek ship, the TARDIS escapes this nightmare landscape which the Doctor thinks may be an immaterial plane somewhere in the dark recesses of humanity's collective consciousness... That or a funhouse in the 1996 Ghanna exhibition.
One suspects that there might be some experimentation going on here. The Chase is only two serials removed from the disastrous Web Planet, where British civilization expressed its collective sigh of progress beyond the Doctor Who fad. The ratings tanked and even the Daleks couldn't quite give it the same gloss. Something new had to be tried, and that evidently included playing up the Doctor's gravest enemies for some quirky laughs.
In that case, one can't blame William Russell and Jacqueline Hill for using the Daleks' time machine for beating a retreat from the series. The previous Dalek serial lost them Susan, and this one loses Ian and Barbara. Once overcoming the Doctor's protective reluctance, the two school teachers learn how to operate the time machine at the end of the last episode and make for Coal Hill in 1965. Like Susan before them, gallivanting with the Time Lord version of Peter Pan is fine for a time, but eventually one wants to live a life with a purpose, responsibilities, small joys and slightly fewer threats of death. The episode ends with a still montage of the duo happily cavorting in the streets of London, checking out police boxes to make sure their captor hasn't returned, and trying to figure out how they are going to explain a two year absence.
The ending is a bit of a tear-jerker insofar as one is happy to see the teachers returned home safely, but also as sad as the Doctor that they are now gone from the show. This story, also the penultimate episode of the second season, brings to an official close that first delightful era of Doctor Who. William Hartnell would hang on for another season and a half, fighting Daleks and rogue Time Lords, going to faraway galaxies and the Old West. The original band has broken up, however. Perhaps the show loses a little direction after this, and it begins a rotating door of companions for the irascible grandfather.
Ian and Barbara's replacement is a human astronaut played by Peter Purves. They meet Steven Taylor on the last leg of the chase, where he has been captive on Mechanus for two years. The TARDIS' crew is taken prisoner by the Mechonoids themselves and Steven explains that this planet was pre-colonized by a group of robots from earth, only to be forgotten by their masters in the course of an interstellar war in which Steven was a pilot. He crashed on the planet, now ruled by the machines.
The Daleks follow them to Mechanus, of course, where they provoke a war of mutual destruction with the Mechonoids. In the chaos the four humans and one Time Lord escape. Steven goes missing, appearing to fall at the hands of the native fungal monsters of Mechanus, yet things are not what they seem, as we'll learn in the next story... an encounter with the Time Meddler.