At her wedding, Daenerys received a chest containing three dragon eggs. These were given to her by Magister Illyrio Mopatis, the man who helped arrange the marriage.
Was it part of a plan? As...
...she managed to hatch the dragons.
We do as of yet not know. In his conversations with Tyrion, he does not seem to have placed much faith in Dany, but it is impossible to say with any certainty, due to the secretive nature of Illyrio and Varys.
I would assume he did not know, just as he did not forsee that Dany would hijack his ships and start a crusade in Slaver's Bay.
Not sure if Illyrio did know, but Dany and Ser Jorah seem to think he didn't; at least not in A Clash of Kings:
“Illyrio believes in no cause but Illyrio. Gluttons are greedy men as a rule, and magisters are devious. Illyrio Mopatis is both. What do you truly know of him?”
“I know that he gave me my dragon eggs.”
He snorted. “If he’d known they were like to hatch, he’d would have sat on them himself.”
That made her smile despite herself. “Oh, I have no doubt of that, ser. I know Illyrio better than you think. I was a child when I left his manse in Pentos to wed my sun-and-stars, but I was neither deaf nor blind. And I am no child now.”
-A Song of Ice and Fire: A Clash of Kings (pg 365), Daenerys.
I think a plot relating to his gift would be beyond the reach of his knowing. There were no portends pointing to that outcome, nor had previous attempts in the later years of the Targs showed any successes in doing the same.
Other potential evidence:
[citations probably needed]
I think he did not know what would happen. He passed them on to Daenerys as a rich, but useless (to him), gift to the beggar Queen of a bloodline renown for dragons. It would carry deep sentimental purpose to her, gaining favor for him, and help re-inforce her legitimacy, if even symbolically.
No, he did not know
In the fifth book, when young Griff were planning the invasion of Westeros, they claimed they were told to wait by Illyrio Mopatis that Daenerys would be joining their cause with a Dothraki horde. No mention of dragons at that time.
“Which plan?” said Tristan Rivers. “The fat man’s plan? The one that changes every time the moon turns? First Viserys Targaryen was to join us with fifty thousand Dothraki screamers at his back. Then the Beggar King was dead, and it was to be the sister, a pliable young child queen who was on her way to Pentos with three newhatched dragons. Instead the girl turns up on Slaver’s Bay and leaves a string of burning cities in her wake, and the fat man decides we should meet her by Volantis. Now that plan is in ruins as well.
So, no mention of Dragons in the first plan. And, if someone like Illyrio Mopatis wanted them, he could have gotten them before they reach Astapor. He sent the ships to Astapor to find her. The mention of dragons in the second plan proves that he had no idea Daenerys could make them hatch. Otherwise, it would be the part of the first plan.
I don't think that Illyrio would have known. But, Varys seems to be pulling Illyrio's strings. I think that Varys might have suspected that the Dany might be able to hatch them.