It seems as though there is a lot of confusion over this topic. What is the difference between ĉar and pro? In what case would I use each word?
pro is a preposition so it should be followed by a noun.
ĉar is a conjunction so it can be followed by a complete phrase.
Both of them indicate that the thing following it is the cause of the thing preceding it. For example:
Mi ne iris eksteren pro la malvarmo.
Mi ne iris eksteren ĉar estas malvarme.
In this case the two phrases are saying more or less the same thing except that in the first case the idea is being expressed as a noun (la malvarmo) and in the second it is a complete phrase (estas malvarme). It would be incorrect to interchange the two words for these sentences:
✖ Mi ne iris eksteren ĉar la malvarmo ✖
✖ Mi ne iris eksteren pro estas malvarme ✖
Note however it is possible and quite common to use pro with a phrase by making it act like a noun by adding tio ke:
Mi ne iris eksteren pro tio ke estas malvarme.
My rule of thumb is that is that when "due to" works in place of "because [of]", then it's pro. Otherwise, ĉar.
Try it with the example sentences others gave, so e.g. "pro la malvarmo" is "due to the cold", thus pro is right, but "pro estas malvarme" would be "due to it's cold", which is wrong, thus use ĉar there instead.