Type a regular expression, or pick a ready-made search and adapt it. Each utterance is matched as the line it is in the transcript, speaker label included (*CHI: …), so the patterns used with grep work here too; you can even paste an old grep -i -E '…' command.
Results come as a concordance, as utterances in context, as charts by age and child, and as the list of forms the pattern matched. The help page has a short guide to regular expressions on CHAT transcripts.