If something such as a law, rule, or action has a chilling effect, it tends to discourage discussion, limit freedom, or cause some other harm.
He has warned of the chilling effect of the new law on free speech. [+ of/on]
There are concerns that the turmoil could soon have a chilling effect on funding for our world-leading research facilities. [+ on]
The demand to pay 50% up front does have a chilling effect.