Ticket:
It is possible to attach/send 25 MB over all ticket attachments via ticket attachment option.
Chat:
It is possible to attach/send 128 MB at once via chat attachment option. However it is very likely that yours or customer's email client won't be able to accept such a large attachment, in case you will be working with the forwarded message or chat transcript.
This size limit is related to SAAS (hosted with us) versions of LiveAgent only.