Seeing stars during daylight?

Is it at all possible to see starts during daylight hours? The reason
I ask is last week, I was in the Adirondack Mts. in New York, at the
annual hot air balloon festival. It was about 5:30 PM and I was lying
on my back, idly gazing ito the sky waiting for the balloons to start
launching. It was a very clear day. I had shielded my eyes from the
sun, which was on it's way down, but was still high enough in the sky
to seem like full daylight, as I watched a wayward kids balloon
sailing away. I suddenly noticed what appeared to be a star almost
directly overhead. I watched it for sometime, waiting to see if it
would move, thinking it was another escaped balloon at a high
altitude. But it remained stationary. I was even able to look away,
then look back and find it. It was clearly visible and looked just
like a star, a pinpoint of light. After a while I lost it, which was
strange as the sun kept setting. But I wondered if under the right
circumstances, one could actually see a star during daylight hours.
Thanks.