The Spanish ship Esperanza and her pirate crew leave Callao Harbor in Peru, loaded with gold and silver bullion looted from Incan temples

The Esperanza gets caught in a storm and suffers a broken mast.  To make matters worse, an independent cruiser, its name unknown, attacks the Esperanza.  The sea battle ends with the attackers victorious, and the surviving Esperanza crew joining the ranks of their captors.  

Accounts differ here on whether it was the attacking vessel or the Esperanza that sank (after transferring her treasure to the surviving ship).  All accounts do agree the treasure was saved and the sailors set sail for Spanish friendly Macao in China, to split the treasure once there.

After 43 days at sea, the sailors encounter a heavy squall and crash on the sunken reefs of an uncharted atoll.  The ship is taking on water, and the main mast broken from the impact.  After 4 days of work, the sailors free the ship enough to sail her one mile to the east, landing on a small island among what they described as "hillocks of land".

Once on the islands of the atoll, the sailors brought the treasure ashore and buried it safely in the sand.  They agree to construct a smaller ship from the remains of the wreck, and sail for help.

After 120 days of effort, a new ship is ready to set sail for help.  Thankfully the rains and lagoons of Palmyra have sustained them, and they're not short on provisions.  Of the 90 remaining survivors, 80 set sail, each taking a small amount of gold.

The vessel is never heard from again.

After waiting on Palmyra for a year with no sign of help, the 10 survivors draw up plans for a small craft in which to seek help.

The men spend 3 months building a ship, and decide 6 should go and 4 will stay to guard the treasure.  They draw lots to determine the 6 leaving, and set off from Palmyra.

After 13 days at sea, 4 of the men are washed overboard in a storm.  As the rain clears, they find their provisions spoiled, but see an American whaler on the horizon, and are able to signal her.  The men are taken onboard, both ill from the journey, but finally rescued.

Both men had become ill at the end of their journey, likely owing to the spoiled provisions, and after just 2 days aboard the whaler, one of the sailors died.  

The Whaler docked in Mission City (modern day San Francisco), leaving the lone survivor in the care of the local mission's hospital.  He gave his name as either James Hines or Edwards, and was supposedly English and well educated.

The sailor lived for 30 days before passing, never leaving his bed.  Before dying, he told his story, and the location of the treasure, to his attendant, a young Chilean-Irish man from Derry, named Conner (or Connor).

Sixty six years later, after a life spent sailing throughout the Americas, Conner ended up in Boqueron, off Callao, Peru, working as the caretaker of a decomissioned Italian man-of-war called the Archimede.  In late 1883, Captain F.D. Walker, a prominent merchant sailor, visited Callao to purchase both the Archimede and a US Navy store ship call the Onward.

He transferred Conner to the Onward, and spent his nights aboard speaking with the old sailor and listening to his sea stories.  One evening, Conner shared his story of the Esperanza and the information he'd been given by the survivor on his death bed.  Not long after, Conner grew ill and was admitted to the hospital, where he died a week later from "old age accelerated by pheumonia".

Nearly 20 years later, after moving his business and interests to Hawaii, F.D. Walker began circulating the story of the Esperanza and how he acquired the information, with local newspapers.  He offered to provide more details on the treasure, to anyone who would fund an expedition to Palmyra.  No such offers were brought forth, and so far as anyone knows Walker never looked for or found the treasure.

While serving as harbormaster of Honolulu, Captain William R. Foster was given an iron chest by a sailor preparing to leave for the Solomon Islands.  He informed Foster the chest was filled with letters and documents detailing the account of the Esperanza, and asked that he keep them safe.

After 20 years without the sailor returning for his chest (its reported he died in the Solomon Islands), Foster decided it was time to share the story.  Much like Walker, he shared the legend as he knew it with local newspapers, but kept the contents of the chest to himself, waiting for someone to propose an expedition to Palmyra.

Unfortunately for him, there had been regular visits to Palmyra since 1902 when Walker first shared the legend, and no treasure had been found, so interest in Foster's material never amounted to anything.