Other commenters have pointed out the problems with overloading of connectors and reduced efficiency because of the added resistance but there is another really important reason not to chain power strips: circuit breakers work best against short circuits when the resistance between the breaker and the short is fairly low (for instance less than 0.5Ω) so that the current will quickly go over the rated current of the breaker. If the resistance is a lot higher because you have too many extensions between the breaker and the fault, the time the breaker needs to react will go up. Counterintuitively this usually means more energy will be turned to heat by the fault.

In extreme cases this can mean the difference between a broken power strip that you can just throw out and a burned down house.