Apollo Radar chain issues
If by 'slip off' you mean that the chain over-rides the sprocket teeth when you apply force through the pedals it's likely that your cassette sprocket teeth are very worn.

Do you know how worn the chan was? As chains wear they elongate, the more elongated a chain gets the more stress and wear it puts on the sprocket teeth.

Check the cassette sprockets for signs of wear to determine if you need to replace the cassette. 

I always recommend getting a chain wear gauge. They are cheap (~$10 US) and easy to use. Avoiding running a worn chain substantially extends the life of the cassette and chainrings.