Transfer encoding 'chunked' was introduced with HTTP version 1.1 and is used when the length of the content is not known up-front, so that no 'Content-length' header can be given. Instead the content is sent in several chunks, each prefixed by the length of the chunk.
It is not related to content-encoding like gzip and both can be used together. It is also not related to a content consisting of multiple parts. In this rarely used cases instead a Content-type of multipart/whatever is used and the client has to split the content by the given boundary, similar to multipart MIME messages in mails.
Any HTTP client claiming support for version 1.1 (like LWP) must support this transfer encoding and there is no way to tell the server not to use it except switching to HTTP/1.0. The Accept-Encoding header only affects the accepted values for Content-Encoding (i.e. compression), not Transfer-Encoding.