Large service providers use load balancers to dispatch millions of incoming connections per second towards thousands of servers. There are two basic yet critical requirements for a load balancer: uniform load distribution of the incoming connections across the servers, which requires to support advanced load balancing mechanisms, and per-connection-consistency (PCC), i.e, the ability to map packets belonging to the same connection to the same server even in the presence of changes in the number of active servers and load balancers. Yet, simultaneously meeting these requirements has been an elusive goal. Today's load balancers minimize PCC violations at the price of non-uniform load distribution. This paper presents Cheetah, a load balancer that supports advanced load balancing mechanisms and PCC while being scalable, memory efficient, fast at processing packets, and offers comparable resilience to clogging attacks as with today's load balancers. The Cheetah LB design guarantees PCC for any realizable server selection load balancing mechanism and can be deployed in both stateless and stateful manners, depending on operational needs. We implemented Cheetah on both a software and a Tofino-based hardware switch. Our evaluation shows that a stateless version of Cheetah guarantees PCC, has negligible packet processing overheads, and can support load balancing mechanisms that reduce the flow completion time by a factor of 2-3 ×.