The bin, located where Silver Lane meets Broad Street, encourages smokers to dispose of cigarette ends in an environmentally friendly way.
The idea is they can have a bit of fun at the same time by answering a question. The first, on bins in both Grantham and Stamford is: Brussels sprouts with Christmas dinner: Yes or No?
SKDC Cabinet Member for Commercial and Operations, Cllr Dr Peter Moseley, said: "Dropped cigarette ends are the most common form of litter in our district. I hope that encouraging smokers to have a bit of fun as they bin their cigarette butts will reduce that.
"The serious side is that cigarette filters contain plastics and other chemicals that don't degrade, and these can be harmful to wildlife if they end up in surface water drains leading to rivers.
"SKDC has pledged to crack down on littering and other anti-social behaviour that can blight our communities. It is part of our work to keep the district looking attractive and clean for residents, visitors and those who work here. Our message is clear: don't drop litter."
A ballot bin which displays a question and two possible replies has already proved a success in Grantham Market Place. Smokers vote by putting their cigarette ends in the slot beneath their preferred answer. The litter stacks up in two columns behind a clear glass front showing which answer is more popular. The last question was X-Factor or Strictly, with X-Factor the clear winner.
The move reflects SKDC's commitment to a Higher Street Standard throughout the district which already consistently exceeds the national average.