You need a double colon AND a blank line between the Example:: section break and the literal block.

See the example from the Napoleon docs:

"""Example Google style docstrings.

This module demonstrates documentation as specified by the `Google Python
Style Guide`_. Docstrings may extend over multiple lines. Sections are created
with a section header and a colon followed by a block of indented text.

Example:
    Examples can be given using either the ``Example`` or ``Examples``
    sections. Sections support any reStructuredText formatting, including
    literal blocks::

        $ python example_google.py

Section breaks are created by resuming unindented text. Section breaks
are also implicitly created anytime a new section starts.
"""

So, in your example, try this:

class Chicken(object):
      """Animal that lays egg and has feathers

         Note:
             Chickens love to eat feed

         Example::

             chicken.eats(feed)
      """