Do employers have the right to not offer sick leave with pay?

I am with a New company that has been open for about 6 months. We just received 5 vacation days. They are saying that we have no paid sick leave allowed and we are not going to be able to accrue any paid sick leave, Even after the 1st year. Only paid time allowed is 3.25 hours every pay period (twice a month) for vacation after another 6 months. Is this legal? I always thought after you worked for a company for at least a year, you could begin to accrue paid sick leave?