No, thats what communism denies.

what do you consider work? do the richest people work harder than factory workers?

I don't doubt that many of the very rich don't work at all. But then again, if it was so easy to become rich, then why doesn't everyone do it? its
because they can't. Its not easy to build a fortune. So yea, Paris hilton is a waste of oxygen, and didn't work for any of her money. And its
unfair that she has so much.

My problem with capitalism, is that almost everyones circumstances are dictated by chance.

I agree, its a problem.

If your parents are rich, you will likely be better educated, etc etc. If you are born stupid, is it your fault?

"Born stupid"? How is that a failing of capitalism?

It's obvious that in the past it was easier to invent something

What? Since when? It was easy for those people? Is that why there are more inventions made faster now than there were in the past?

, yet, do you choose when you are born?

Thats not a problem specific to Capitalism either, it'd still exist in a communist society

we're not meant to have governments

Says who? By man's nature the existence of government is assured. Its practically a trait amoung all primates, let alone hierarchical chimps and
then man. No type of society exists(or at least has been found) without some form of governement. And is this supposed to be a problem with
Capitalism? Capitalism doesn't require government. Capitalism is all about governement staying
laissez faire, not becomming more invovled.
Heck if government didn't exist, capitalism wouldn't even notice it. Whereas under communism, governement is what everything is.
Capitalism in this sense is sort of like what winston churchill said about democracy. its the worst system we have, except for all those other ones.
Having said that, I would not argue for completely unregulated untempered unrestrictde 'true'
laissez faire free markets. The US's take of
a 'mixed economy' seems to work quite well, and the 'european' welfare state system also has had good successes in moderating businesses excesses
and whatnot.