The whole notion of loyalty inquisitions is a natural characteristic of the police state, not of democracy. Knowing his rule rests upon compulsion rather than consent, the dictator must always assume the disloyalty, not for a few but of many, and guard against it by continual inquisition and liquidation of the unreliable. The history of Soviet Russia is a modern example of this ancient practic. The democratic state, on the other hand, is based on the consent of its members. The vast majority of our people are intensely loyal, as they have amply demonstrated. To question, even by implication, the loyalty and devotion of a large group of citizens is to create an atmosphere of suspicion and distrust which is neither justified, healthy, nor consistent with our traditions. […] I must, in good conscience, protest against any unnecessary suppression of our ancient rights of free men. Moreover, we will win the contest of ideas that afflicts the world not by suppressing those rights, but by their triumph. We must not burn down the house to kill the rats.

Adlai Stevenson (1900-1965) American diplomat, statesman

Veto Message, Illinois State Senate Bill 102 (1951-06-26)
    (Source)

The Broyles Bill would have required all public workers, teachers, and officials, as well as candidates for office to sign loyalty oaths. Its veto by Stevenson, as Illinois Governor, was widely used by his political enemies during the Red Scare of the era.

This quote is widely misidentified as a more generic comment condemning the federal McCarran Internal Security Act of 1950. I've been unable to find any primary source connecting this quotation to that event.

It is often elided and paraphrased down, e.g.:

The whole notion of loyalty inquisitions is a national characteristic of the police state, not of democracy. I must, in good conscience, protest against any unnecessary suppression of our rights as free men. We must not burn down the house to kill the rats.