Q:

What was said by swami Vivekananda about Hinduism in Chicago Speech?

He has given a great speech about Hinduism and makes feel proud of us on our culture and Hinduism. I have only always one thing in his that speech "All my dear Brothers and Sisters". I didn't hear anything else.
Here, I just want some brief description of his speech.

A:

There are actually many addresses which were given by Swami Vivekananda at Chicago. The one that you're referring to was given on September 11, 1893.
You can download this PDF. It contains the addresses.

Chicago, 11 September 1893
Sisters and Brothers of America, It fills my heart with joy
  unspeakable to rise in response to the warm and cordial welcome which
  you have given us. I thank you in the name of the most ancient order
  of monks in the world; I thank you in the name of the mother of
  religions; and I thank you in the name of the millions and millions of
  Hindu people of all classes and sects. My thanks, also, to some of the
  speakers on this platform who, referring to the delegates from the
  Orient, have told you that these men from far
  -off nations may well claim the honour of bearing to different lands the idea of toleration. I am proud to belong to a religion which has
  taught the world both tolerance and  universal  acceptance.  We 
  believe  not  only  in  universal toleration, but we accept all
  religions as true. I am proud to belong to a nation which has
  sheltered the persecuted and the refugees of all religions and all
  nations of the earth. I am proud to tell you that we have gathered in
  our bosom the purest remnant of the Israelites, who came to southern
  India and took refuge with us in the very year in which their holy
  temple was shattered to pieces by Roman tyranny . I am proud to belong
  to the religion which  has  sheltered  and  is  still  fostering  the 
  remnant  of  the grand Zoroastrian nation. I will quote to you,
  brethren, a few lines from a hymn which I remember to have repeated
  from my earliest boyhood, which is every day repeated by millions of
  human beings:   As the different streams having their sources in
  different places all mingle their water in the sea, so, O Lord, the
  different paths which men take through different tendencies, various 
  though  they  appear ,  crooked  or  straight,  all  lead  to Thee.
   The present convention, which is one of the most august assemblies
  ever held, is in itself a vindication, a declaration to the world, of
  the wonderful doctrine preached in the  Gita : Whosoever comes to Me,
  through whatsoever form, I reach him; all men are struggling  through 
  paths  which  in  the  end  lead  to  Me. 2 Sectarianism, bigotry,
  and its horrible descendant, fanaticism, have long possessed this
  beautiful earth. They have filled the earth with violence,  drenched 
  it  often  and  often  with  human  blood, destroyed civilization, and
  sent whole nations to despair . Had it not been for these horrible
  demons, human society would be far more  advanced  than  it  is  now .
  But  their  time  is  come;  and  I fervently hope that the bell that
  tolled this morning in honour of this convention may be the
  death-knell of all fanaticism, of all persecutions  with  the  sword 
  or  with  the  pen,  and  of  all uncharitable feelings between
  persons wending their way to the same goal.

