One dark night, as the camera pans across a dark, empty forest, Bugs Bunny is heard singing a stanza of Sweet Dreams, Sweetheart. When the camera zooms in on Bugs' rabbit hole, he pokes up out of his hole, dressed in a nightshirt and holding up a candle, and tells the audience, "Eh, I don't know but, did you ever have the feeling you was being watched?," which he is, via remote TV, as an evil scientist (a caricature of Hollywood actor, Peter Lorre) is planning to catch a rabbit to provide dinner for his large, hairy, orange, sneaker-wearing monster named Gossamer. The scientist lures Bugs to his castle via a shapely robotic female rabbit, complete with a large wind-up key in the back, and accompanied by Oh, You Beautiful Dollin the cartoon's underscore. Once Bugs gets to the castle (labeled "evil scientist" in neon lights) the evil scientist locks the door behind him. Bugs looks at him and says, "You don't need to lock that door, mac. I don't wanna leave." Then he clicks his tongue and raises his eyebrows at the audience and begins kissing the mechanical rabbit on the hand. The robot short-circuits and breaks into pieces. Bugs faces the audience and says, "That's the trouble with some dames...kiss 'em and they fly apart!"
Nonchalantly shrugging off this odd encounter, Bugs heads for the door, but the scientist persuades him to stay and meet another "little friend". When it becomes clear that this "friend" is a ferocious beast, Bugs sizes up the situation, vigorously shakes the scientist's hand "Goodbye!" and launches into a schtick where he packs luggage for a vacation trip, accompanied by a very brassy rendition of California, Here I Come. Just before bolting for the door, he tells the scientist, in typical Groucho Marx-esque fashion, "And don't think it hasn't been a little slice of heaven...'cause it hasn't." The scientist then releases Gossamer. This is the last scene featuring the scientist, as the rest of the cartoon is an extended chase between Bugs and Gossamer, with gags aplenty. At one point, as Bugs is behind a door and Gossamer is trying to break through, a desperate-sounding Bugs cries out, "Is there a doctor in the house?" A silhouette, seemingly from the theater audience, stands up and offers, "I'm a doctor." Bugs suddenly relaxes, grins, starts munching a carrot, and asks, "What's up, Doc?," just before Gossamer breaks through and the chase resumes.
Bugs Bunny and Gossamer pass by a mirror; Gossamer looks at the mirror, then his reflection runs away toward the door, screaming in horror; Gossamer looks at the audience and shrugs. Bugs rushes up a staircase, but rushes back down and knocks down Gossamer, telling him he can't go up there because it's dark. Bugs acts as a lamp; he dances to the tune of Shuffle Off To Buffalo and taunts Gossamer by calling "Hey, Frankenstein!". Bugs and Gossamer keep running until a door on the floor opens and a rock falls into the empty space. While Bugs is tiptoeing backwards and praying, he bumps into Gossamer. He comes up with an idea and gives him a manicure. After filing Gossamer's nails, Bugs says, "Now let's dip our patties in the water!," and puts the monster's fingers into the water to have his fingernails cut, but it contains two mousetraps. Gossamer yelps in pain and starts sobbing.
Bugs twice thinks he has escaped. The first time, the monster is hiding behind a picture frame and Bugs apparently isn't aware until he wises up and pokes Gossamer in the eyes. Gossamer gets out from behind the wall, and while looking for Bugs, finds him in a painting. Gossamer then gets the idea to poke Bugs in the eyes too, but before he can fully carry it out, Bugs jumps the gun and pokes Gossamer in the eyes again, and disappears from the painting, making Gossamer go behind the wall again. The second time, Gossamer is following Bugs behind the wall (which Bugs knows is happening because Gossamer is copying Bugs' footsteps) until Bugs marks where he previously was and smashes the mark with a giant mallet when Gossamer appears behind it. The wall crumbles and a barely conscious Gossamer quickly follows.
The third time, Gossamer's in a knight's armor, holding an axe above his head. He gets hit by Bugs Bunny in his locomotive-style knight-riding horse, causing him to hit the wall to turn into a can labeled "Canned Monster". However, as Bugs saunters off toward the exit, singing to himself, Gossamer gets the bunny in his clutches. Bugs repeats his opening line, "Did you ever have the feeling you were being watched?", and Gossamer's expression changes from anger to anxiety, and Bugs points to the audience. Gossamer (despite having already acknowledged the audience earlier) shrieks, "PEOPLE!" and runs away screaming, breaking through a series of walls, leaving his cartoon outline in all of them. Having "re-re-disposed of the monster", Bugs is about to "exit stage right" (although he's actually going stage left), when the female robo-rabbit re-appears, intact, and again accompanied by Oh, You Beautiful Doll.
Bugs snickers, "Mechanical!," but then the robot smooches him on the cheek, leaving a lipstick mark on the smitten bunny, who says, "Well, so it's mechanical!," and assumes a robot-like gait (with his tail magically rotating like the robot's wind-up key) and follows her off the screen.