You can always use bleach to chlorinate your pool. Dichlor simply adds stabilizer, which you can get separately at any pool store, and probably K-Mart, Costco, WalMart, Sears, etc. It's called stabilizer or conditioner, but the only ingredient should be cyanuric acid or Isocyanuric acid, aka CYA.

Bleach + CYA = Same Effect as adding Dichlor.