Mr Deby, who took power in a coup 26 years ago, is seen by Western governments as a bulwark against Islamist militants in central Africa.
In the run-up to the election, security was stepped up, with protest marches banned and activists imprisoned.
Despite Chad's new oil wealth, half its 13 million people live in poverty.
The opposition boycotted the last election in 2011, allowing Mr Deby an easy victory, while this year his chances of winning again have been strengthened by fractures in the opposition.
One prominent opposition activist, Ngarlejy Yorongar, was banned from standing.
A referendum in Chad in 2005 scrapped a clause restricting presidents to two terms but Mr Deby says he will reinstate it if re-elected.
"Our country is starting from a long way back but the future looks bright," said Mr Deby as he voted. "I ask all politicians to respect the verdict of the ballot box."
Results are not expected for two weeks, according to a timetable set out by the electoral commission.
Record low international oil prices and the growing cost of anti-terror operations in the region are among the country's main challenges.
Chad's army is seen by western governments as an important contributor to the fight against Islamist militants in the region.
Both Nigeria's Islamist group, Boko Haram, and al-Qaeda in the Islamic Maghreb are seen as threats.
The authorities have also been trying to suppress unrest this year over delays in the payment of civil servants' salaries and a recruitment freeze.
In the run-up to the vote, protest marches were banned and activists campaigning against the president were jailed. Mr Deby is also accused of favouring his own ethnic group - the Zaghawa.
However, the president's message of stability has won him support.
"We came to vote for the president to guarantee peace in our country," civil servant Fatima Zara told Reuters news agency in the capital N'Djamena as she lined up to vote.
"Around us in the neighbouring countries there are too many problems."
Those allowed to stand against Mr Deby include opposition leader Saleh Kebzabo, campaigning on a platform of change.
Mr Kebzabo has said he has proof of large-scale fraud in the elections.
Votes are being counted in Chad after a presidential election widely expected to deliver President Idriss Deby a fifth term in office.