Analysts say the legal challenge has little chance of success given the courts' historic tilt towards the ZANU-PF, which has ruled since independence from British colonial rule in 1980.
The MDC party alleges that the vote result was rigged and President Emmerson Mnangagwa's narrow victory was due to a falsified vote count in Zimbabwe's first election since the end of Robert Mugabe's rule.
The court will have 14 days to make a ruling on the case.
The MDC must prove that any irregularities were grave enough to change the outcome of the vote.
The President-elect is expected to appoint a new Cabinet after his inauguration scheduled for Sunday. "We have a good case and cause".
Mr Chamisa wants the court to declare him the victor or call a fresh election, his lawyer told Reuters news agency on Friday.
Britain's Minister for Africa Harriett Baldwin said in a statement she had spoken to Chamisa and Zimbabwe's Foreign Minister Sibusiso Moyo to urge calm while the election challenge was being considered by the court.
The conduct of the election was largely deemed sound by worldwide monitors, but representatives of the European Union noted Mnangagwa benefited from an "un-level playing field" and some voter intimidation.
"We've managed to place before the court forms that show the (results) figures were erased", MDC party lawyer Thabani Mpofu told reporters.
"In the alternative, we seek that there be another election which complies with the dictates of the law", Mpofu said.
"I am confident they have no case", Zanu PF PF legal secretary Paul Mangwana said.
Earlier this month, Mnangagwa secured a comfortable victory, according to results from the Zimbabwe Electoral Commission, polling 2.46 million votes against 2.15 million for the 40-year-old Chamisa.
At least six people were killed in violence that erupted after the vote as security forces clashed with and MDC supporters who alleged that Mr Chamisa had been robbed of victory.