This is the code we use to do it.  It may be outdated, but it still works for us.
 

public with sharing class Chat_Controller {
    public static String TRANSCRIPT_KEY = 'transcript';
    public static String NICK_SEPERATOR = ':';
    public static String LINE_SEPERATOR = '\n';
    public static String LINE_TEMPLATE = '<p>__LINE__</p>';
    public static String NICK_TEMPLATE = '<b>__NICK__' + NICK_SEPERATOR + '</b>__LINE__';

    public String getFormattedTranscript() {
        String transcript = '';

        PageReference pageRef = ApexPages.currentPage();

        if (!pageRef.getParameters().containsKey(TRANSCRIPT_KEY)) {
            return transcript;
        }

        String transcriptPre = pageRef.getParameters().get(TRANSCRIPT_KEY);

        List<String> lines = transcriptPre.split(LINE_SEPERATOR, -1);

        for (String line : lines) {
            String result = '';

            List<String> splitNick = line.split(NICK_SEPERATOR, 2);

            if (splitNick.size() == 2) {
                result = NICK_TEMPLATE.replace('__NICK__', splitNick.get(0)).replace('__LINE__', splitNick.get(1));
            } else {
                result = line;
            }

            transcript += LINE_TEMPLATE.replace('__LINE__', result);
        }

        return transcript;
    }
}

where the page uses the Chat_Controller and has the following to output the transcript
 

<apex:outputText escape="false" value="{!formattedTranscript}" />