Hideki trying to find Chii's ON switch, as well as the said switch's location.
Hideki hopping on a cow and shouting "I'm gonna go to Tokyo!" at the beginning of the first episode.
The whole sequence where Chi and Sumomo are wandering around the city trying to buy underwear. Those two are comedy gold together.
Chii's singsong "Underpants, underpants..."
In the original Japanese, it's even funnier. She just keeps walking, saying, "Pantsu...pantsu..." in a tone that is an interesting mix of a chant, a mantra, and a marching theme. Absolutely hilarious.
Chii mistaking a lingerie ad and the panties of a couple of schoolgirls for her goal.
Chii picking up Sumomo like a dog just did.
Chii returning home from her task with underwear for Hideki, with the phrase "good job" on the front.
Hideki finally getting the courage to enter the lingerie shop, and the only thing that can come out of his mouth is an Ironic Echo of what he told Chii to say:
Underpants thank you please!" * ka-ching!*DAAAAAAAAAAAAHHHHH!
"Pervert! Hideki is a pervert!" "Chi, you don't have to learn that!!"
In the English dub: "Average size! Hideki is average!"
When Hideki is first trying to teach Chi to talk, he starts with his name, pointing at himself and saying "Hideki." Then she also points at him and says "Hideki," and for a moment he thinks the lesson has been successful... until she starts pointing at random objects around the room while saying "Hideki! Hideki! Hideki! Hideki!"
Funniest one may be when she calls his landlady "Hideki".
From the manga: "Can Chi do this job?" Bonus points for the Call Back.