As the number of observed gamma-ray bursts (GRBs) continues to grow, follow-up resources need to be used more efficiently in order to maximize science output from limited telescope time. As such, it is becoming increasingly important to rapidly identify bursts of interest as soon as possible after the event, before the afterglows fade beyond detectability. Studying the most distant (highest redshift) events, for instance, remains a primary goal for many in the field. Here, we present our Random Forest Automated Triage Estimator for GRB redshifts (RATE GRB-z ) for rapid identification of high-redshift candidates using early- time metrics from the three telescopes onboard Swift. While the basic RATE methodology is generalizable to a number of resource allocation problems, here we demonstrate its utility for telescope-constrained follow-up efforts with the primary goal to identify and study high-z GRBs. For each new GRB, RATE GRB-z provides a recommendation—based on the available telescope time—of whether the event warrants additional follow-up resources. We train RATE GRB-z using a set consisting of 135 Swift bursts with known redshifts, only 18 of which are z > 4. Cross-validated performance metrics on these training data suggest that åisebox-0.5ex 56% of high-z bursts can be captured from following up the top 20% of the ranked candidates, and i̊sebox-0.5ex 84% of high-z bursts are identified after following up the top rs̊ebox-0.5ex 40% of candidates. We further use the method to rank 200 + Swift bursts with unknown redshifts according to their likelihood of being high-z.