ICs ("chips") are typically packaged in what material?
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.