This famous sonnet was written in October 1816 and first published in the Examiner on 1 December 1816.  It is considered the highlight of Keats's first volume of poetry.  It was originally a gift for his friend, Charles Cowden Clarke.  The two men had spent an evening reading George Chapman's superb translation of the Iliad and Odyssey.  The next morning, Clarke came down to breakfast and found the sonnet waiting for him.  As he later recalled:

'A beautiful copy of the folio edition of Chapman's translation of Homer had been lent me.... and to work we went, turning to some of the 'famousest' passages, as we had scrappily known them in Pope's version.... Chapman supplied us with many an after-treat; but it was in the teeming wonderment of this his first introduction, that, when I came down to breakfast the next morning, I found upon my table a letter with no other enclosure than his famous sonnet, 'On First Looking into Chapman's Homer.'  We had parted, as I have already said, at day-spring, yet he contrived that I should receive the poem from a distance of, may be, two miles by ten o'clock.'

On a historical note, Vasco Núñez de Balboa discovered the Pacific Ocean, not Cortez.

Please note the alteration Keats made before publication to the seventh line.

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The original manuscript image of John Keats's 'On First Looking into Chapman's Homer':

 

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Much have I travell'd in the realms of gold,
    And many goodly states and kingdoms seen;
    Round many western islands have I been
Which bards in fealty to Apollo hold.
Oft of one wide expanse had I been told
    That deep-brow'd Homer ruled as his demesne;
    Yet did I never breathe its pure serene
Till I heard Chapman speak out loud and bold:
Then felt I like some watcher of the skies
    When a new planet swims into his ken;
Or like stout Cortez when with eagle eyes
    He star'd at the Pacific--and all his men
Look'd at each other with a wild surmise--
    Silent, upon a peak in Darien.