If your HTTP request is simple then Phill's answer will suffice, but if the request is not so simple, the browser will send a preflight check. The preflight check is an OPTIONS HTTP request and this has to be handled too.
Here is an extension method to configure CORS:
public static class MyNancyExtension
{
    public static void EnableCORS(this Nancy.Bootstrapper.IPipelines pipelines)
    {
        pipelines.AfterRequest.AddItemToEndOfPipeline(ctx =>
        {
            if (ctx.Request.Headers.Keys.Contains("Origin"))
            {
                var origins = "" + string.Join(" ", ctx.Request.Headers["Origin"]);
                ctx.Response.Headers["Access-Control-Allow-Origin"] = origins;
                if (ctx.Request.Method == "OPTIONS")
                {
                    // handle CORS preflight request
                    ctx.Response.Headers["Access-Control-Allow-Methods"] =
                        "GET, POST, PUT, DELETE, OPTIONS";
                    if (ctx.Request.Headers.Keys.Contains("Access-Control-Request-Headers"))
                    {
                        var allowedHeaders = "" + string.Join(
                            ", ", ctx.Request.Headers["Access-Control-Request-Headers"]);
                        ctx.Response.Headers["Access-Control-Allow-Headers"] = allowedHeaders;
                    }
                }
            }
        });
    }
}
To enable CORS call this extension method in the bootstrapper:
protected override void ApplicationStartup(Nancy.TinyIoc.TinyIoCContainer container, Nancy.Bootstrapper.IPipelines pipelines)
{
    base.ApplicationStartup(container, pipelines);
    pipelines.EnableCORS();
}
Please note it is not extending NancyModule because OPTIONS is handled outside of module (also here).