Short answer. Yes, within a limit. The Civil Code says a lease may run for a period that is definite or indefinite, so a fixed end date is not required. But it also caps duration absolutely: no lease for more than ninety-nine years is valid.
What the law says
In the lease of things, one of the parties binds himself to give to another the enjoyment or use of a thing for a price certain, and for a period which may be definite or indefinite. However, no lease for more than ninety-nine years shall be valid.
Civil Code, Article 1643 — Lease of Things, and the Ninety-Nine-Year Ceiling. Read the full provision →
A lease need not have a fixed end date
The definition of a lease of things in the Civil Code expressly allows an open-ended term. It says one party binds himself to give another the enjoyment or use of a thing for a price certain, and for a period which may be definite or indefinite. So a lease is not invalid merely because the parties never wrote down an exact end date. A definite lease runs to an agreed day; an indefinite one has no such date fixed at the outset. Both are recognised. What a lease always needs is a price certain, the rent, because the arrangement is the use of the thing in exchange for that price.
But no lease may exceed ninety-nine years
Indefinite does not mean unlimited. The article sets a hard outer boundary: no lease for more than ninety-nine years shall be valid. This is an absolute ceiling that the parties cannot lengthen by agreement. A lease purporting to run for, say, a century and a half, or one drafted to be perpetual, exceeds what the law will enforce as to duration. The ninety-nine-year cap reflects a policy against tying up property forever in one leasehold arrangement, keeping ownership from being permanently hollowed out by an endless lease that never returns full control to the owner.
How an open-ended lease is actually measured
An indefinite lease being permitted does not leave the parties with no term at all. Where the length has not been fixed, the Civil Code supplies a period based on how the rent is paid: for ordinary urban leases, a lease with rent paid monthly is understood to run from month to month, and so on down to daily rent. Article 1687 is the provision that fills this gap, and it also lets courts extend the term in some situations once a tenant has occupied the property for a certain time. So 'no fixed end date' usually resolves into a recurring period rather than a lease that literally never ends.
What this means for your lease
For most people the practical takeaway is twofold. First, a lease without a stated end date is valid, but it will be read as running period to period according to how rent is paid, which affects how and when it can be ended. Second, if a lease is written to last beyond ninety-nine years, the excess will not hold. If your goal is long-term security or, conversely, a clean way to end an open arrangement, the wording of the period clause does real work. It is worth having the lease drafted or reviewed with those consequences in mind before you sign.