
Claxon |

Not if the other creature is unaware of the invisible creature.
As Attacks of Opportunity interrupt the provoking action and resolve prior to it, any available AoO would occur before grappling actually occurred. At least that's how it's playing out in my understanding of the rules.
Also, if you don't know a creatures location you can attempt to attack it but it requires you to select a square and deal with the miss chance (which you will still have as the creature is invisible).
Edit: Excellent, Sniggevert found the rules text I was thinking of but couldn't locate to have a more definite no. Thanks for that. I was looking under invisible and blinded conditions. I didn't think to look under concealment rules.

Icyshadow |

No. You can not take an AoO against something with total concealment.
PRD on Concealment wrote:You can't execute an attack of opportunity against an opponent with total concealment, even if you know what square or squares the opponent occupies.
So RAW states that it isn't possible, because an invisible creature has total concealment.

Numarak |
Under concealment rules:
You can't execute an attack of opportunity against an opponent with total concealment, even if you know what square or squares the opponent occupies.
So: if you can not see the invisible attacker, you can't make attacks of opportuniy against her. Same situation under darkness and no darkvision.
I would say:
RAW no.
RAI no.
Edit: I'm slower than a crippled snail.

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I would like to point out that once the invisible attacker does initiate the grapple, he is no longer invisible as grappling is an offensive action. (though Greater Invisibility would keep him invisible)
It would be to late to get an AoO, but easier to hit him with one handed/light weapons on the grappled characters turn.

Byakko |
If they do remain invisible (say, from Greater Invis), keep in mind that:
A grappled creature cannot use Stealth to hide from the creature grappling it, even if a special ability, such as hide in plain sight, would normally allow it to do so. If a grappled creature becomes invisible, through a spell or other ability, it gains a +2 circumstance bonus on its CMD to avoid being grappled, but receives no other benefit.