Short answer. Usually not. Article 754 says the donor is generally not obliged to warrant the things donated, so if a third party lawfully takes the property, you ordinarily cannot claim against the donor. There are exceptions — an onerous donation, and the donor's bad faith — and you are subrogated to the donor's own rights.
What the law says
is not obliged to warrant the things donated, save when the donation is onerous, in which case the donor shall be liable for eviction to the concurrence of the burden
Civil Code, Article 754 — Warranty And Eviction In Donations. Read the full provision →
The general rule: no warranty in a gift
A donation is an act of pure generosity, so the law does not hold the giver to the same warranty a seller owes a buyer. Article 754 puts it plainly: the donor is not obliged to warrant the things donated. This means that if a third person with a better right comes along and evicts you — lawfully takes the donated property away — you generally cannot turn around and demand that the donor make good your loss. Having received the property for nothing, the donee ordinarily bears the risk that the donor's title was imperfect. Gratuitousness cuts both ways.
You step into the donor's shoes
Although the donor usually owes no warranty, you are not left without any recourse. The article opens: The donee is subrogated to all the rights and actions which in case of eviction would pertain to the donor. Subrogation means you inherit whatever legal rights and actions the donor himself would have had against others in the event of eviction. So if the donor had a claim against a prior seller, a warrantor, or another party, that claim passes to you. It is not a claim against the donor, but the donor's own remedies against third persons become yours to pursue.
When the donor is liable after all
The no-warranty rule has two express exceptions. First, an onerous donation — one where you had to give or do something in return, a burden. Here the article says the donor shall be liable for eviction to the concurrence of the burden: to the extent of what you were charged, the donation resembles an exchange, so warranty applies up to that value. Second, bad faith: the donor shall also be liable for eviction or hidden defects in case of bad faith on his part. A donor who knew of the flaw in title and stayed silent cannot hide behind the gift's gratuitous character.
What this means for your situation
So whether you can claim against the donor depends on the kind of donation and the donor's conduct. If it was a pure, freely given gift and the donor acted in good faith, you generally cannot recover from him for a third party's eviction — though you may pursue the donor's transferred rights against others. If the donation was onerous, the donor answers up to the burden you bore; and if the donor acted in bad faith about the title or defect, he is liable despite the gift. Identifying which category fits is the starting point.