Author: Michael Dworetsky <mmd@star.ucl.ac.uk>
 
The short answer is no (well, almost no).  The long answer is given by
David Hughes in the Quarterly Journal of the Royal Astron. Soc., 1983,
vol. 24, pp 246-257.

This mistaken notion was first mentioned by Aristotle and other
ancient sources, and was widely assumed to be correct by many literary
sources of the 19th century, and even believed by some astronomers.
But every astronomer who has ever tested this by experiment came away
convinced it was impossible.

If you want to try an interesting experiment to see why it is believed
that whatever people see up chimneys cannot be stars, try the
experiment at night, as I have done, using a cardboard tube centre
from a paper towel roll (mine had an opening of 25 square degrees).
You will see that, at random, you will seldom include one visible
star, rarely two, and virtually never more than two, in the field.

Separate experiments to attempt to see Vega and Pollux through tall
chimneys were performed by J. A. Hynek and A. N.  Winsor.  They were
unable to detect the stars under near perfect conditions, even with
binoculars.

The daytime sky is simply too bright to allow us to see even the
brightest stars (although Sirius can sometimes be glimpsed just after
the Sun rises if you know exactly where to look.)  Venus can be seen
as a tiny white speck but again, you have to be looking exactly at the
right spot.

The most likely explanation for the old legend is that stray bits of
rubbish get caught in the updraft and catch the sunlight as they
emerge from the chimney.  It is possible to see stars in the daytime
with a good telescope, as long as it has been prefocused and can be
accurately pointed at a target.