A partial boner; What a male usually acquires in a dry hump situation with a female. Can also occur when one sees something fucking hot, for example three female German models playing twister but-ass nekked. Other connotations of the phrase include: 3/5ths chub, thirder (1/3 chub), and halfie. Remedies for the removal of quarter chubs include being punched square in the kids and/or seeing Star Jones on television. Personally, I prefer the former.
1) "Wow Barbara! I believe our dance just afforded me with a quarter chub! Your work is far from over."
2)"Dude, get up I want pizza."
"I can't! I've got a halfie!"
"Oh. I'm gonna go hit on your sister then"
"I'm good now. How about Dominoes?"