Can I find Halal meat or products in supermarkets?

Hello Adam! 

There are halal products available in some Japanese supermarkets, but it can sometimes be hard to find. 

However there are some supermarkets like Gyomu supermarket and several online stores that sells Halal meat and other food products. 

check these out!

Gyomu supermarket, several locations available in Tokyo, here are two examples:

Ueno Okachimachi : 2 Chome-3-4 Ueno, Taito, Tokyo 110-0005

Shin Okubo: 2 Chome-15-1 Hyakunincho, 新宿区 Tokyo 169-0073

And here are two halal online shops: 

http://www.onlinehalalfood.com/

http://www.baticrom.com/ 

Hope these are useful!