Sorry to bump this but I've posted a more in depth description of this problem on the WP forum but don't seem to be getting any interest there either.
I'm not saying it is an issue with Thematic per se - I'm just interested to know if anyone can reproduce the issue or even if they can find the same problem with their own child themes in Google Chrome. Here is my WP post in full:
Theme: Thematic as parent theme
Plug-in: WP Supercache
In the above set up Google Chrome shows a marked delay when loading pages with the child theme active. The delay is made worse by the fact that the screen goes blank while pages load (there is minimal content in either of my installs - more below).
I have tried this with custom code in the child theme's functions.php and also with a blank child theme (effectively running Thematic defaults via the child theme) either way the loading is slow even with WP Supercache activated.
Everything goes back to normal if I revert to using Thematic as the main theme - quick page loading with no blank screen between page loads.
Hopefully someone might want to try to reproduce this at home; I have set up two basic installs of WordPress with identical configuration on two different web hosts:
In the former install the delay is constant and very noticeable.
In the latter install the caching seems to kick in after a couple of page views but the blank screen should be noticeable initially before things settle down (the performance is still not as good as it should be in Chrome).
The odd thing is that I have tried viewing these sites in Firefox (versions 2 and 3+) Safari, IE 6, 7 and 8 (all on Win XP). In all these browsers both installations load as quickly when the child theme is active as they do when Thematic is the main theme.
I'll try to leave both installations alone for a couple of days in the hope that someone gets to look at them.