A panel of 14 grand justices will hear a debate over a disputed law that critics say is unconstitutional because it prevents unions between gay couples.
Campaigners for change gathered with rainbow flags outside the court in Taipei, which was heavily guarded Friday morning.
"Gay people as citizens deserve equal rights and protections under the law," 24-year-old salesman Lan Shi-kai told AFP.
Two petitions for an interpretation of Taiwan's Civil Code have been brought by veteran gay rights activist Chi Chia-wei and the Taipei city government, which has been receiving a growing number of requests to register gay marriages.
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"The constitutional court's decision is legally-binding," Hsieh Kuo-lien, a law professor at National University of Kaohsiung, told AFP.
"If its decision is favourable to gay rights activists, it would be effectively legalising same-sex marriage."
At the centre of the case is a clause in the Civil Code which says an agreement to marry should be made between a man and a woman.
Authorities in Taiwan have been rejecting applications for same-sex marriages based on this clause.
The court will hear arguments over whether that part of the Civil Code contravenes elements in Taiwan's constitution which guarantee equality and freedom of marriage.
A legislative committee approved an amendment to the civil law that would allow gay couples to legally tie the knot.
That bill is now due for a second reading.
Taiwan is considered progressive on many issues including gay rights, however its roots in Confucianism translate into a strong sense of adherence to traditional mores.
There has been growing momentum behind the campaign to change the law.
However, the debate has also split society, with conservative groups saying allowing same-sex unions would destroy family values.
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