Yes
Toxic, and a very potentially toxic one at that, bitter amygdalin. However, this substance is also widely distributed in the seeds of almonds, apple seeds and other plants in the Rosaceae family. Hydrolysis of this bitter substance can produce cyanide, and cyanide poisoning can indeed trigger headaches, nausea, vomiting and other symptoms, and in severe cases can lead to breathing difficulties and even death.
It's important to note that the amount of bitter amygdalin in cherry kernels is much lower than in bitter almonds, and even if you chew five of them, it's hard to have a serious toxic reaction.
Overall, the toxicity of cherry pits only manifests itself when a sufficient number of pits are chewed and swallowed slowly.