Why are integrated circuits called "chips"?

Integrated circuits (IC) are called by many chips, and as a particular case, microprocessors are also nicknamed chips. The same happens in Hebrew, where ICs are called "shvav" (or "shvavim" in plural), which is the Hebrew word for a chip.

What is the source for the nickname?

Solution 1:

ODO says chip is short for microchip.

Definition of microchip
noun
  a tiny wafer of semiconducting material used to make an integrated circuit.

Thus chip has its normal meaning of "a small piece" (of silicon, in this case) and microchip is a tiny piece.

Even if the shortening of microchip is discounted, at the heart of each IC package is a tiny chip of silicon.