Michael Chong sometimes seems like he's running for the Conservative Party leadership in the hardest possible way.

Last week, while most Conservative MPs were struggling with Liberal motion M-103 on condemning Islamophobia, Mr. Chong supported it, saying that after January's shooting at a Quebec City mosque, it's time to study anti-Islamic prejudice. And the centrepiece of his leadership campaign is a steep carbon tax – in a party that has for years dubbed such policies a "tax on everything."

Mr. Chong tells party members they need those kinds of policies to win the 2019 election. But sailing against the prevailing wind probably makes it hard for him to win the leadership. Carbon taxes make many Conservatives jeer. Some suggest he might have the wrong party. But Mr. Chong insists he is in many ways the most conservative candidate in the race.

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"This, to me, feels like 1984," Mr. Chong said in an interview in his Parliament Hill office. He's referring to the period before Brian Mulroney's Tories embraced free trade, which is now part of its fibre. "To me, the issue of climate change and a conservative approach to reducing emissions is the same kind of fight."

Mr. Chong is best known for three things, and all involved clashing with parts of his own party. The first was resigning as Stephen Harper's intergovernmental affairs minister in 2006 over the prime minister's decision to recognize Quebec as a nation. The second was his campaign for a democratic-reform bill aimed at giving backbenchers more power. The third is running for the leadership on a carbon tax.

He isn't the kind of politician who spouts slogans he won't explain. He's the kind who will argue for his policies for hours. And while some of his leadership-campaign competitors ape Donald Trump's populism in various ways, Mr. Chong argues that the rise of populist politicians makes his democratic-reform agenda more important. "We need to ensure that we have institutions that can put proper checks and balances on a future prime minister that may want to push the boundaries of their power," he said. But his campaign will turn on his climate change plan: a huge levy that would reach $130 a tonne by 2030 – balanced by a massive, immediate $18-billion income-tax cut.

Mr. Chong argues it is the conservative approach to climate change. It would replace other green regulations, shrinking government. It would be revenue neutral, financing deep income-tax cuts that he argues will stimulate the economy and allow Canada to compete with tax cuts that Mr. Trump and U.S. Republicans will offer south of the border.

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"This is increasingly an economic question. And we've got to get this question right, or we're going to damage the economy," he said.

It's hard to say how he's doing. There are few reliable polls of party members, and none that adequately reflect the complex system with a preferential ballot and equal weighting of ridings. Mr. Chong was third in fundraising behind Maxime Bernier and Kellie Leitch by the end of 2016, before reality TV star Kevin O'Leary joined the race. Some guess he is in a second tier behind those three. But Mr. Chong is running against headwinds. When candidates were asked about climate-change policy at a debate in Halifax two weeks ago, 12 of the 14 just said they were against a carbon tax. That seemed to be popular. His carbon tax sometimes raises groans. Conservatives were used to campaigning against carbon taxes under Mr. Harper. In Alberta, Premier Rachel Notley's version has drawn ire from the right. Mr. Chong argues his would not be the same, because it would be revenue neutral, and points to Conservatives such as Preston Manning and Mr. Harper's former policy director, Mark Cameron, who support a carbon tax. In the United States, former Republican secretaries of state James Baker and George Schultz have called for a carbon tax.

In Ontario, Progressive Conservative Leader Patrick Brown supports a carbon tax, too. But that's a defensive strategy: Centrist voters in Ontario won't take him seriously if he doesn't have a climate policy, one strategist said, but inside the party, it doesn't win members' hearts. In other words, climate policies can help Conservatives win elections, not leadership races. But Mr. Chong argues party members can be persuaded. "Does the party want to win in 2019?" he asked. "I think it does. If Conservatives don't have a credible policy on emissions, a credible policy on climate change, we cannot win the 2019 election."