This happens every year in early June, and the resulting Arietid meteor shower typically peaks on June 7th. If you could turn off the sun, you would see more than 60 meteors per hour, making it one of the most active showers of the year. No one is sure where Arietid meteoroids come from, although some astronomers suspect they are debris from sungrazing asteroid 1566 Icarus. Another candidate is comet 96P/Machholz.
In fact, there is way to see a few of these meteors. Try looking just before sunrise. The shower's radiant (labeled ARI in the radar map above) rises in the east about 45 minutes before the sun. At that time of day, Arietids tend to be "Earthgrazers," i.e., meteors that skim horizontally through the upper atmosphere from radiants near the horizon. Spectacular Earthgrazers are usually slow and bright, streaking far across the sky--a real eye-opener. Sky maps: northern hemisphere, southern hemisphere.