Although the country's founding legal document has been tweaked several times since it was enacted in 1980, those calling for change say a new text is key to safeguarding social rights and establishing citizen participation in the young democracy.
Those opposing the change say the current Magna Carta has given stability to Chile and there are more pressing demands to be addressed.
Why change the constitution?
The main argument is symbolic: The existing document was written and approved during the military dictatorship and lacks legitimacy, its critics say. The text leans toward a conservative interpretation of the law and provides no formal avenues for citizens to participate in political decisions.
Any changes to the constitution, including involving such issues as access to healthcare, water rights, pensions or the power of the Constitutional Court, require up to a two-thirds approval by Congress.
Constitutional lawyer Jaime Bassa, a professor at the University of Valparaíso, said reforms had failed to the tackle the central chapter of the constitution that deals with fundamental rights.
"The political project that the dictatorship embedded in the constitutional text remains in force," he said.
"The entire system of protection of social rights, specifically social security, health, education, work and trade union cover is marked by a preference for private property and freedom of entrepreneurship."
Another controversial issue in Chile is the veto power the Constitutional Court has over public policies. "That has caused political agreements reached in Congress to later be pushed back to the Constitutional Court," said María Cristina Escudero at the University of Chile Institute of Public Affairs.
For example, last year the court rejected a move by right-wing parties to block a law legalizing abortion in some cases, but added a clause that allowed hospitals and clinics to refuse to perform procedures.
What would the change process look like?
"Constitutions do two things: They create power and limit it," said Escudero.
The current constitution does not stipulate who can decide for it to be replaced, the people through a referendum or Congress. It also does not pronounce on whether any replacement should be drawn up by a people's assembly, a mixed commission of politicians and citizens, or Chile's Congress, in which the ruling center-right coalition holds just under half the seats in both houses.
Previous attempts at reform have dragged. President Sebastian Pinera's center-left predecessor, Michelle Bachelet, sought to strip the document of traces of authoritarianism and create town-hall groups to discuss constitutional change and pave the way for a new constitution. Days before leaving power in early 2018, she sent the plan to Congress, but it remains bogged down at the committee stage.
Unanimous demands for plebiscite
Protesters are largely unanimous in their demand for a plebiscite on replacing the constitution, which, once approved, should be drafted by a people's assembly.
The idea of a plebiscite is a popular one in Chile since a popular vote ended Pinochet's military dictatorship after he asked whether he should stay in power. The result was a resounding no.
The current constitution limits the issues that can be put to a referendum, and whether to replace it is not on the approved list.
Experts say this clause could be changed by Congress to open the door to a plebiscite.
If there were to be a popular vote, Fuentes said, it could contain a second question of who should draft the new document.
"In the current context, when politicians, Congress and political parties are so discredited, I believe that citizens would favour a mixed commission or a Constituent Assembly," he said.
Others argue that a plebiscite should only take place to approve any new document that has been drafted.
Javier Sajuria, a Chilean and senior politics lecturer at Queen Mary University of London, said citizens should vote on a "concrete proposal, not a vague idea." He added: "If you don't believe me, look at Brexit."
Chile's right-wing parties have historically rejected the notion of a new constitution, and this week Pinera's Chile Vamos coalition voted down one of a series of constitutional reforms moving through Congress.
However, there are a "growing number of parliamentarians" whose eyes have been opened by the fervent popular protests wracking Chile who are now more open to mixed formulas or a Constituent Assembly, said Fuentes.
Another key demand of protesters has been the resignation or removal of President Piñera. But he, too, is limited in what he can do by the constitution.
Chile's president is elected by direct vote for a period of four years. If, due to illness, absence from the territory or "other serious reason," he cannot exercise his position, the interior minister is to stand in for him.
If the president faces a motion to remove him in Congress, this must be approved by a majority in the Chamber of Deputies and then by two-thirds of the Senate.
If the president wants to resign, the Senate must decide "whether the reasons that originate it are founded or not and, consequently, allow or dismiss it." Before that, however, senators should hear the opinion of the Constitutional Court.