The paper considers a coded caching setup with two libraries and where only one of them needs to be kept secret from an external eavesdropper. We provide upper and lower bounds on the secrecy rate-memory tradeoff for systems with K = 2 or K = 3 receivers. Our bounds are tight in some regimes and show that the standard (non-secure) coded caching upper bound can be approached for a wide range of parameters. In some cases, the proposed upper bound on the secrecy rate-memory tradeoff is even lower than the lower bound for standard coded caching. The reason is that in our setup the ratio of receivers requesting secure files over those requesting nonsecure files is fixed and known to everyone in advance. The transmitter can thus adjust the contents stored in the cache memories to this ratio.