What is the size of drive chain I need for a 1979 Harley Davidson XLH 1000?

You maybe correct, the pawl spring (one of them) may be broken or contaminated with gunge. Before delving in too deep, make sure the selector is free and lubricated.
Sorry to say, removal of the chain case and then remove the clutch assembly, primary chain and then after removing the final drive to the main drive chain, remove the gearbox. Replace the pawls and springs.

You'll have to count the number of links you need from the old chain. You may can use a "stock" number of links chain if you are sure your bike has 'stock" sprockets on it. If the sprockets have been changed, you may need more or fewer number of links. I'd order the longest one I could get and then cut the chain to length.

Good Luck
Steve