The research led by Hiromitsu Nakauchi, Professor of Genetics at Stanford University, is the first of its kind to receive government approval after Japan changed its rules on implanting human cells into animals.
Japan previously required researchers to terminate animal-human hybrids within 14 days but changed the restriction in March this year,
"It took nearly 10 years, but we are now able to start the experiment," said Prof Nakauchi.
Previously scientists had hoped that pig or sheep organs could be used directly because they are roughly the same size as a human.
However they were always rejected. The new approach gets round the rejection problem because it uses stem cells directly from a human patient.
The Salk Institute in the US has already created human-pig hybrids but no lab has yet succeeded in growing an organ.
In the Salk Institute experiments researchers created embryos where one in 100,000 cells were human, but the new Stanford embryos would have one in 10,000 human cells.
Prof Nakauchi said it could still take several years to reach a stage when a human heart could be harvested from a pig or sheep, but has already successfully grown a mouse pancreas in a rat.
"Although we have shown proof-of-concept studies using rodent models, to overcome the genetic distance between human and pig is not easy," he said.
"The study is just about to begin. Do not expect that we are generating human organs in a year or two."
And there are also ethical issues to the research. If human cells accidentally end up in the brain or reproductive system scientists would have to halt work while the ethics of continuing were debated.
Prof Nakauchi said his team would be proceeding with extreme caution given the ethical concerns.
"We will have two checkpoints during embryonic development of chimeras," he added.
"At each step we examine embryos for the presence of human cells in the brain. After confirming the absence or few human cells, we go to the next step."