All the thoughts I had got increasingly convoluted. Obviously stuff like: zcat /var/log/syslog* | head -n1 .. doesn't achieve what I want...
for a in /var/log/syslog*gz;do zcat $a 2>/dev/null|head -n 1;done
If you want to know which file the line came from:
for a in /var/log/syslog*gz;do echo "$a: $(zcat $a 2>/dev/null|head -n 1)";done