Short answer. No. Article 872 forbids the testator from imposing any charge, condition or substitution whatsoever on the legitime — the share the law reserves for a compulsory heir. If you attach one anyway, it is considered as not imposed: your child still takes the legitime, free of the condition you tried to add.
What the law says
The testator cannot impose any charge, condition, or substitution whatsoever upon the legitimes prescribed in this Code. Should he do so, the same shall be considered as not imposed.
Civil Code, Article 872 — But Never on the Legitime. Read the full provision →
What Article 872 protects
Article 872 provides that the testator cannot impose any charge, condition, or substitution whatsoever upon the legitimes prescribed in this Code. Should he do so, the same shall be considered as not imposed. The legitime is the portion of the estate the law sets aside for compulsory heirs — children, in the usual case, and also the surviving spouse and, where relevant, ascendants. It is theirs by force of law, not by the testator's grace. The article makes that reservation untouchable: the testator may not dilute, delay or burden it with strings of any kind.
How wide 'whatsoever' reaches
The word 'whatsoever' is doing deliberate work. The ban is not limited to obviously hostile conditions; it covers charges, conditions and substitutions alike, benign or not. A direction that the child must reach a certain age, marry, or manage the property a certain way — even a well-meant trust over the share, or a substitution naming who takes it next — all fall on the legitime as forbidden burdens. The testator's freedom to attach conditions belongs to the free portion, the part of the estate he may dispose of as he likes. Over the legitime he has no such latitude at all.
The remedy: the burden falls, the share stays
Notice what the article does with an offending condition. It does not void the gift of the legitime or send the share elsewhere; it strikes only the condition, which is considered as not imposed. So the compulsory heir takes his full legitime exactly as if nothing had been attached to it. The testator cannot use an impossible or unwelcome condition to force a child to renounce the share, because the condition simply evaporates and the share remains. This makes the protection self-executing: the heir need not perform anything, and the burden cannot be enforced against him.
Where a testator's wishes can still operate
None of this leaves a testator powerless — it just channels his conditions to the right property. Charges and conditions may be validly attached to gifts out of the free portion, so a parent who wants to encourage or restrain a child can do so with the disposable part of the estate rather than the reserved part. The practical step, when drafting, is to keep the two masses distinct: satisfy each compulsory heir's legitime cleanly and unconditionally, and place any conditions on what is given beyond it. A condition written across the whole estate will simply drop away insofar as it touches a legitime.