Neat script. I have one small enhancement. It will enable the use of the enter key to submit the just-typed message. (It's only an added convenience.)
Unfortunatley javascript would be needed to refocus the cursor after the submission. (like google does)

Howto:
Replace this section of code:

    print $c start_html, h1("Chat write");
    print $c start_form(-action => "$url/write");
    print $c textfield("name","[I must change my name]", $NAME_MAX),
       submit("says:"), textfield("message", "", $MESS_MAX, $MESS_MAX,
+ 1);
    print $c end_form;
[download]

With this section of code:

    print $c start_html, h1("Chat write");
    print $c start_form(-action => "$url/write");
    print $c textfield("name","[I must change my name]", $NAME_MAX), s
+ubmit("Change Name");
    print $c end_form;
    print $c start_form(-action => "$url/write");
    print $c hidden("name","[I must change my name]", $NAME_MAX), subm
+it("says:"), textfield("message", "", $MESS_MAX, $MESS_MAX, 1);
    print $c end_form;
[download]

And it still falls under 100 lines (just not as much).