Is it possible to keep adding C and H atoms to make longer and longer chains to an infinite number?
You are probably thinking of alkanes of the form CnH2n+2. They have been named as large as C(100)H(202).
According to an archived entry in Wikipedia, which seems to make sense to me:
" ..at absolute zero, you could actually make a hydrocarbon chain infinitely long (as long as you have enough stuff). But in practice, when you can't actually get to absolute zero, there's a theoretical upper limit on how long you can make the chain due to entropy. That is, the higher the temperature and the longer the chain, the less stable it is."