Setting border-radius on the #map div does not affect the map itself. Not sure if this is a bug in Webkit, Leaflet, or expected behavior. Looks good in Firefox and IE 9.

This is a browser bug. :( Not possible to fix from Leaflet side as far as I know. I wanted to add border radius to examples on the website but no luck...
Same thing here with Chrome only. I just put a 1px white border around the map div and it's good enough for me. As long as it's a light map. Not worth the effort to research with my skill set.
I got this to work in chrome (v38.0.2125.122) by adding z-index: 0 to the map container if that helps anyone.
@gwithian wow, really surprised that this fixes it.
Thank you so much for this answer <3
Hey, I tried @gwithian trick and it works well, even with another value. Seems that just to specify a z-index make it work (Chrome Version 49.0.2623.112 )
@gwithian thanks, it works
@gwithian this neat little trick works in Safari too - thanks!
Most helpful comment
I got this to work in chrome (v38.0.2125.122) by adding
z-index: 0to the map container if that helps anyone.