We ran into the same issue. You need to reference the record type ID so your content should look something like this:

`input type="hidden" name="liveagent.prechat:caseRecordType" value="0121a0000001nX3"`

`input type="hidden" name="liveagent.prechat.findorcreate.map:Case" value="RecordTypeId,caseRecordType"`

`input type="hidden" name="liveagent.prechat.findorcreate.map.doCreate:Case" value="RecordTypeId,true"`

`input type="hidden" name="liveagent.prechat.findorcreate.showOnCreate:Case" value="true"`


I've left a record type ID in there just for the sake of the example, but just go to your record type and grab what you want to open.