Try onkeyup event like this:
<%@ Page Language="C#" AutoEventWireup="true" CodeFile="Default2.aspx.cs" Inherits="Default2" %>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title></title>
<script type="text/javascript">
function check() {
var textboxcontent = document.getElementById("<%=TextBox1.ClientID%>").value.trim();
document.getElementById("<%=CheckBox1.ClientID%>").checked = (textboxcontent.length > 0);
}
</script>
</head>
<body>
<form id="form1" runat="server">
<div>
<asp:CheckBox ID="CheckBox1" runat="server" />
</div>
<p>
<asp:TextBox ID="TextBox1" runat="server" onkeyup="check()"></asp:TextBox>
</p>
</form>
</body>
</html>