Fair Chance at Housing Act of 2019 This bill limits the authority of public housing agencies (PHAs) to deny or terminate federally assisted housing based on criminal conduct by the applicant or tenant. Specifically, PHAs may deny or terminate assistance based only on criminal conduct that threatens the health or safety of other tenants or the employees or owner of the PHA, excluding misdemeanors and certain other lesser criminal offenses. Furthermore, with respect to applicants, a denial may be based only on a felony conviction other than a conviction for a drug offense for which the individual served less than 10 years. Before denying or terminating assistance based on criminal conduct, a PHA must conduct an individualized review and consider specified factors, including evidence of rehabilitation. PHAs must also give the household an opportunity to remove the culpable member before proceeding with the denial or termination. Additionally, PHAs may not drug test applicants or tenants as a condition of assistance. Under current law, PHAs must deny, and may terminate, federally assisted housing upon a determination that any household member is illegally using a controlled substance. Current law also allows PHAs to take such actions if there is reasonable cause to believe that a household member's illegal use of a controlled substance or abuse of alcohol may interfere with the health, safety, or right to peaceful enjoyment of the premises by other residents. Further, tenants evicted on the basis of drug-related criminal activity are not eligible under current law for federally assisted housing for three years, unless the tenant successfully completes a rehabilitation program.