Title says it all. I've tried searching on google without a definitive answer.
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Supposed to be a maritime-related deal, with traders from the British East India company returning to the West from Malaysia bringing a recipe for something called kicap (pronounced: "kee-chap," with variable spellings and ingredients). Circa 17th cent. Of note is that the original was probably the same thing now available in Asian markets, called Nampla or Nuk-nam, a fermented fish sauce.
Also of interest is modern-day usage of both "catsup" and "ketchup."
To supplement @The Raven's solid answer, I offer these:
Ketchup, OED, 1711
The OED says:
Their earliest quotation is 18th century:
But they have an earlier quotation for catchup:
I found a 10-year antedating in The mysteries of opium reveal'd by John Jones (1701) which uses it twice. First on page 350:
And page 358:
A later antedating gives a hint of the content, in Philosophical Transactions of the Royal Society of London (1708 - Volume 25 - Page 2268):
This is undocumented, but I heard that the term 'ketchup' originated with spice traders who travelled in Southeast Asia/ Hong Kong/ Canton province. In Cantonese, the term 'chup' means literally 'sauce'. In the provincial areas of Canton, tomatoes are called "Fan Ke". In a slang phrase, Ke-Chup or Ket-Chup means tomato sauce.
First, the Amoy pronunciation of 鮭汁 is kê-chiap, meaning salmonidae juice.
Then, the pronunciation travels to Malaysia, and use the spelling kechap, and changes the meaning into tomato sauce.
Next, the pronunciation travels to the Netherlands, and spells as ketchup.
Finally, English use the ketchup spelling from Dutch.