Configurações necessárias para (de)serializar classes do pacote java.time com o Jackson 2.x em uma API implementada com JAX-RS 2. Testado com o Wildfly 8.2.0.Final.

JacksonJavaTimeConfiguration.java

@Provider
public class JacksonJavaTimeConfiguration implements ContextResolver<ObjectMapper> {  
    private final ObjectMapper mapper;

    public JacksonJavaTimeConfiguration() {
        mapper = new ObjectMapper();
        mapper.registerModule(new JSR310Module());
        mapper.configure(SerializationFeature.WRITE_DATES_AS_TIMESTAMPS, false);
    }

    @Override
    public ObjectMapper getContext(Class<?> type) {
        return mapper;
    }  
}

trecho-pom.xml

<dependency>
	<groupId>com.fasterxml.jackson.datatype</groupId>
	<artifactId>jackson-datatype-jsr310</artifactId>
	<version>2.4.1</version>
</dependency>