Final opinion polls indicate his centre-right Democratic Alliance (AD) is ahead of the Socialist Party (PS) and is likely to pick up more votes but once again fall short of the 116 seats needed in Portugal's 230-member parliament to obtain a ruling majority.
Polling stations opened at 08:00 am (0700 GMT), with exit poll results expected at 08:00 pm after they close.
The election in the European Union member state of around 10 million comes at a time when the bloc is grappling with global trade tensions and seeks to beef up its defences.
“We have to do our part at home and we have to be part of the solutions abroad, in Europe and in the world. And for that we need a strong government,“ he said.
He had proposed the confidence vote himself had proposed following accusations of conflicts of interest stemming from his consultancy business.
Montenegro has denied wrongdoing, saying has not been involved in the running of the consultancy, which he has now passed on to his children.
Toughened immigration policy
But only one in five voters feel the case is “very important” and 29 percent think it has no importance at all, according to a final pre-election opinion poll carried out by Lisbon’s Catholic University.
“It hasn’t really had the dimension that the opposition would have hoped for in the campaign,“ she added.
Under a previous Socialist government, Portugal became one of Europe's most open countries for immigrants.
Montenegro's government announced during the campaign the expulsion of some 18,000 irregular immigrants, leading to accusations it was pandering to far-right voters and taking a page from the playbook of US President Donald Trump playbook.
But Chega has also faced embarrassment, including allegations that one of its lawmakers repeatedly stole luggage from airport carousels.
He was rushed to hospital both days but made a surprise appearance at the party's final event on Friday.
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