Short answer. Yes, unless your lease says otherwise. Article 1656 lets the lessor of a business or industrial establishment continue engaging in the same business or industry the lessee is using the leased property for, unless there is a stipulation to the contrary in the lease agreement itself.
What the law says
The lessor of a business or industrial establishment may continue engaging in the same business or industry to which the lessee devotes the thing leased, unless there is a stipulation to the contrary.
Civil Code, Article 1656 — Lessor of a Business May Continue the Same Trade. Read the full provision →
The default rule lets you keep competing
Article 1656 answers this directly, and in the landlord's favor by default. It provides that the lessor of a business or industrial establishment may continue engaging in the same business or industry to which the lessee devotes the thing leased, unless there is a stipulation to the contrary. Simply leasing out your store to someone who then runs a particular kind of business there does not, by itself, stop you from running the same kind of business yourself elsewhere, even in competition with your own tenant.
The lease can take that freedom away
This default only holds when the lease is silent on the point. The article's own phrase, unless there is a stipulation to the contrary, means the parties are free to agree otherwise. If your lease contains a non-compete clause, or some other provision restricting you from engaging in the same business while the lease is in force, that agreement controls instead of the default rule, and you would be bound by whatever limits you actually agreed to.
Why the default favors the lessor
Leasing out a property for a specific kind of business does not automatically mean the owner is giving up their own right to work in that same trade or industry. Absent an explicit agreement restraining competition, the law does not read that restriction into the lease on its own, because restricting someone's livelihood or business activity is a significant limitation that should be the product of a clear, deliberate agreement rather than something implied from silence.
What this means before you open a competing shop
Check your lease agreement with your tenant for any clause addressing competition or restricting your own business activities while the lease is in effect. If there is no such stipulation, Article 1656 supports your right to continue engaging in the same business or industry, even nearby, despite having leased out this particular establishment to someone now running that same kind of business there. If you want that freedom preserved beyond doubt, or want it restricted going forward, addressing it explicitly in the lease removes any ambiguity for both sides.