integrated circuit - ICs ("chips") are typically packaged in what material?

ICs are typically packaged (encapsulated) in a black "plastic". What is this packaging material made of?

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Answer

Transfer-molded epoxy (which is a thermoset material).

Thermoset plastics, once cross-linked will not melt, they only char at high temperatures.

See, for example, this TI/NS document:

As mentioned in the NS document above, epoxy cresol novolac (ECN) is the most common ingredient of these epoxies.

(source)

Link to fire at Sumitomo in Japan in '93.