Why would it have a chilling effect on immigrants?  Unless, of course, you intentionally left out one defining word, illegal, in your statement.  An illegal immigrant is not to be conflated with an immigrant regardless of how or how often the left attempts to do so.  They are not one and the same.  Those who have committed crimes already have a chilled relationship with law enforcement.  That they make themselves a more inviting target of other criminals by their own criminal behavior is not the fault of society, it is the result of the choices they themselves have made to violate the law.  There is an easy remedy to the situation, live your life in accordance with the laws of the society.  Then you needn't worry about having a "chilled" relationship with the law enforcement officers.