Old English cipp "small piece (of wood, stone etc.) separated from a body by a blow from an instrument," perhaps from PIE root *keipo- "sharp post" (source also of Dutch kip "small strip of wood," Old High German kipfa "wagon pole," Old Norse keppr "stick," Latin cippus "post, stake, beam;" the Germanic words perhaps were borrowed from Latin).
Meaning "small disk or counter used in a game of chance" is first recorded 1840. Meaning "piece of dried dung" first attested 1846, American English. Electronics sense "thin, tiny square of semi-conducting material" is from 1962.
Used for thin slices of foodstuffs (originally fruit) since 1769; specific reference to potatoes (what Americans would call French fries) is found by 1859 (in "A Tale of Two Cities"). The fish-and-chips combination was being offered in London by 1860. Potato-chip is attested by 1854, but the context doesn't make it clear whether this is the British version (above) or the U.S. version, "very thin slice of potato fried until crisp" (the British crisp), which is said to have been invented 1853 in Saratoga, N.Y., and is described, more or less, by this name in a recipe book from 1858.
Chip of the old block, familiar term for a child or adult who resembles a parent in some way is used by Milton (1642); earlier form was chip of the same block (1620s); more common modern form of the phrase with off in place of of is by early 20c. To have a chip on one's shoulder is 1830, American English, from the custom of a boy determined to fight putting a wood chip on his shoulder and defying another to knock it off. When the chips are down (1940s) is from the chips being down on the table after the final bets are made in a poker match. Chips as a familiar name for a carpenter is from 1785.