。
Fat hens don't lay eggs.
Literal
Fat chickens [topic-は] eggs [object-を] lay-not.
A proverbial observation — prosperity or excess leads to unproductivity. 肥えた鶏 modifies 鶏 with the past participle of 肥える. 卵を産む means 'to lay eggs.'
。
Fat hens don't lay eggs.