The poster is headlined ‘What don’t you like about free trade, Mrs May?’ and states that free trade means getting rid of tariffs.
It is being displayed in 880 JDW pubs across England, Scotland, Wales and Northern Ireland.
JDW founder and chairman Tim Martin claimed ending tariffs would reduce shop and pub prices, as well as improving living standards.
He said: "There will be a huge gain for business and consumers if the UK copies the free-trade approach of countries like Singapore, Switzerland, New Zealand, Australia, Canada and Israel, by slashing protectionist EU import taxes on leaving the EU in March next year.
"It is not often that the Government can enrich the electorate without losing tax income, however, this is a rare example.
"These invisible tariffs are charged on more than 12,000 non-EU products, including rice, oranges, coffee, wine and children's clothes. The proceeds are collected by the UK taxman and sent to Brussels.
"If Parliament votes to end tariffs and rejects the 'Chequers Deal', consumers and businesses will benefit additionally by avoiding a cost of £39bn, or £60m per UK constituency, in respect of the EU divorce payment, for which there is no legal obligation.”
Martin said some individuals, businesses and business organisations have “mistakenly or misleadingly” repeated the “myth” that food prices will rise without a Brexit deal.
He added: “In fact, the only way prices can rise post Brexit is if parliament votes to impose tariffs.
"The EU will have no say in the matter, provided that the government does not sign away the UK's rights in a deal in the meantime."