To find the number of moles of chlorine in 134.5 grams, we can use the following formula:
```
number of moles = mass / molar mass
```
Substituting the given values into the formula, we get:
```
number of moles = 134.5 g / 70.9 g/mol = 1.9 mol
```
Finally, to find the number of molecules of chlorine in 1.9 mol of chlorine, we can use Avogadro's number, which tells us that there are 6.022 x 10^23 molecules in 1 mole of any substance. Multiplying the number of moles by Avogadro's number, we get:
```
number of molecules = 1.9 mol * 6.022 x 10^23 molecules/mol = 1.15 x 10^24 molecules
```
Therefore, there are 1.15 x 10^24 molecules of chlorine in 134.5 grams of chlorine.