"Perchance to Dream" is the ninth episode of The Twilight Zone. It was written by Charles Beaumont and starred Richard Conte. It was first broadcast in November of 1959.
The first praise I can give to this episode is that it took me a long time to figure out what was going on. Much like when I first watched "Where Is Everybody?", my first few guesses about what direction the plot was heading were all wrong. Some of the misdirection and suspense were built up through cinematography that is almost nauseous: although it is unrelated to the main plot, some sped up shots of a revolving door at the beginning of the episode set the viewer's mind into a frenetic, confused mindset.
Mood being established, we proceed to our plot: a man who is afraid of falling asleep goes to visit a psychiatrist. He has a heart condition that might be triggered by a strong shock, and he has intrusive thoughts that if he lays down to sleep, something in a dream could trigger this shock. He begins to describe his past dreams to his psychiatrists, dreams that become increasingly tense.
Since this is a Twilight Zone episode, we know there is a twist ending. But more important than that is the way the episode sets its mood: it has a fast, frenetic pace, and has some scenes where the implications of sex, drugs and violence are quite strong for 1959. This episode is another episode that shows the growth in the scope of The Twilight Zone.