Same here: I can confirm that this behavior started after auto-updating to Chrome 7. Use web client 5.0.18 build 20090707. A few additions:
1. If you've set your preferences to compose email in HTML, this problem also occurs when you compose a new email (not just when replying).
2. There's a ticket for this problem in the Chromium project since Oct 1:
Issue 57566 - chromium - Zimbra compose is broken - Project Hosting on Google Code. The more Chrome users star this issue, the higher its priority.
3. There's a workaround. If you change the status of the signature back and forward, you can type in the message field.
Needless to say it is a serious problem, because it makes the use of the web client in Chrome very difficult.