No. But, there is a provision in the DOL’s Field Operations Handbook called the “time-off plan”. I will start this answer by saying I am not a fan of the Time-Off Plan. But, that does not negate the fact that this little-known provision is valid and still published in the DOL’s Field Operation Handbook.
We see the rule for private sector employers which is very limited but accurate on page 38 – The Time Off Plan https://www.dol.gov/whd/FOH/
Here are some older articles by 2 well-known employment law sites that explain the “time-off” plan.
In the case of Dunlop v. New Jersey, the court made the following comments:
13 The Wage-Hour Administrator has considered the question of compensatory time off as a form of overtime compensation. In Opinion Letter No. 913 (December 27, 1968), he explained:14 “An employer may not credit an employee with compensatory time (even at a time and one-half rate) for overtime earned Which is to be taken at some mutually agreed upon later date subsequent to the end of the pay period in which the overtime was earned, rather than pay cash for the overtime as it is earned. However, it is permissible for the employer employing one at a fixed salary for a fixed workweek to lay off the employee a sufficient number of hours During some other week or weeks of the pay period to offset the amount of overtime worked (i.e. at the time and one-half rate) so that the desired wage or salary for the pay period covers the total amount of compensation, including overtime.” (emphasis added).15 We conceive this restrictive endorsement of compensatory time off to be perfectly consistent with the language and goals of the FLSA as well as the regulations surrounding it. The restriction that time off for overtime be granted within the same pay period as earned mirrors the stricture placed upon monetary payments for overtime.
I hope this helps clear up the question. I am not suggesting that “comp time” is legal if the private sector. But, the Time-Off Plan is legal if administered properly.