While you're replacing the chain, I recommend replacing the freewheel at the same time. Two reasons for this:

1. A new chain on an old freewheel might cause skipping, either immediately or soon thereafter. Not only that, it could cause premature chain wear.

2. A Shimano freewheel, coupled with a modern chain, will provide superior shifting than you're accustomed to, even with friction shifting.

Get a genuine Shimano freewheel. You won't be disappointed. And coming from me, a Shimano detractor, this really says something.