The first usage for this expression that I could find in a legal context is in Justice Goldberg’s concuring opinion in New York Times Co. vs Sullivan (1964):
"The opinion of the Court conclusively demonstrates the chilling effect of the Alabama libel laws on First Amendment freedoms [301] in the area of race relations."
Mr. Sullivan, the police commissioner in Montgomery Alabama, sued the NY Times (deep pockets) for libel over a paid advertisement that appeared in the newspaper. The state courts found for Mr. Sullivan, but the Supreme Court reversed.
(Interesting side note: this case might have ended differently if the newspaper had been the London Times and the courts were in the UK)
In Keyishian v. Board of Regents (1967), Justice Brennan’s opinion defines more clearly what creates the "chilling effect":
"‘the threat of sanctions may deter . . . almost as potently as the actual application of sanctions.’ NAACP. v. Button, supra, at 433. The danger of that chilling effect upon the exercise of vital First Amendment rights must be guarded against by sensitive tools . . . ."
In this case loyalty oaths as a condition of employment were struck down on free speech grounds.
Of course, "chilling effect" referring to physical or weather phenomena has a longer history.
Cheers,
BNJTOKYO
