sed
$ sed 's/.../&\n/g' file.txt
grep
$ grep -oE '.{1,3}' file.txt
ABCDEFGHIJKLMNOPQRSTUVWXYZ
$ echo abcdefghi | dd cbs=3 conv=unblock 2>/dev/null abcdefghi
Just with bash:
while read -n 3 chars; do printf "%s\n" "$chars"; done < file.txt > new-file.txt