A glaring problem I've been thinking about lately, and I'm surprised I haven't seen any discussion on it, is the growing size of the block chain.

The transaction ledger grows each day, and because it's permanent, eventually it will get very computationally expensive to move a single coin because it has a huge transaction history built up on it.

Am I missing something here? To me it seems that over time the global block chain will grow in size to the point where it consumes all computing resources thrown at it. Home PC's can't be expected to store multi-gigabyte (or terabyte) block chains just to perform transactions.

Am I completely off-base here?