Get your chain sized right, and your derailleur adjusted correctly.

I'm not sure I follow your terminolgy, but it sounds like you had it in th Big/Big combination (i.e. the biggest front ring, and the biggest rear ring) This is called cross chaining, and you typically want to avoid it because it puts a bit more wear on the components, and can be noisier.

If the chain isn't long enough and you put it into the big/big combination, you can start ripping things apart, which I am guessing is what you did.

Even though you don't want to typically ride around cross chained, you need the chain to be long enough to comfortably go into the Big/Big combination without damage, to avoid just the incidient you experienced.

Go to Park Tools or Sheldon Brown's website, and they will explain how to size your chain.