You can use the Deployment API to pass the account parameters using javascript on the webpage.
You need to add the following 2 lines before the liveagent.init(..) method.
liveagent.addCustomDetail('Account_Name', 'GenePoint');
liveagent.findOrCreate('Account').map('Name','Account_Name',true,true,false);
You can add more fields to perform search. A more complete example from documentation can be found at the following link.
Creating Records Deployment API Code Sample
Full code from the sample VF page that I created to test this.
As soon as the chat is initialized, the system searches for an Account called GenePoint and displays the detail page automatically.
<apex:page>
<a id="liveagent_button_online_573i0000000NZnE" href="javascript://Chat" style="display: none;" onclick="liveagent.startChat('573i0000000NZnE')">ONLINE</a><div id="liveagent_button_offline_573i0000000NZnE" style="display: none;">OFFLINE</div><script type="text/javascript">
if (!window._laq) { window._laq = []; }
window._laq.push(function(){liveagent.showWhenOnline('573i0000000NZnE', document.getElementById('liveagent_button_online_573i0000000NZnE'));
liveagent.showWhenOffline('573i0000000NZnE', document.getElementById('liveagent_button_offline_573i0000000NZnE'));
});</script>
<script type='text/javascript' src='https://c.la2c1.salesforceliveagent.com/content/g/js/32.0/deployment.js'></script>
<script type='text/javascript'>
liveagent.addCustomDetail('Account_Name', 'GenePoint');
liveagent.findOrCreate('Account').map('Name','Account_Name',true,true,false);
liveagent.init('https://d.la2c1.salesforceliveagent.com/chat', '572i0000000NXE8', '00Di0000000jydC');
</script>
</apex:page>