Paddy Murphy, who also runs a village pub in Ballymore Eustace, Co Kildare, has been overwhelmed by the interest after a YouTube video of his new arrival went viral.
The hybrid - sometimes referred to as a geep or a shoat - is believed to be extremely unusual.
Mr Murphy said he delivered the animal late at night, and it was only the next morning that he realised it was a bit different.
"I only have white-faced Cheviot sheep, and when this one came out it was black," he said.
"That sometimes happens. But the next morning I said to myself this isn't a lamb at all, it's more like a goat."
He added: "It was moving a bit too quickly for a lamb, its legs were very long and he even has horns like a goat."
Mr Murphy said he noticed a goat mating with his sheep on the mountainside but assumed nothing would come of it.
The newborn has been the talk of the village pub. A video by the Irish Farmer Journal posted on YouTube video has reached nearly 15,000 hits.
Mr Murphy said he was hoping to raise money for a sick child in the village with a competition for the best name for his young geep.
And he has invited scientists to come to his farm to prove the rare cross-breed.
"I have no interest in that side of it at all, but if someone wants to come and do tests they are welcome," he said.
Similar crossings have been reported before in Chile, Jamaica, Malta and in Botswana, where scientists found a hybrid - known as the Toast of Botswana - had 57 chromosomes, a number in between that of sheep and goats.
In most cases the offspring is stillborn.