Попробуйте с JSON.stringify.
var chiavi = [];
chiavi[0] = ["A", "B"];
chiavi[1] = ["C", "D"];
$.ajax({
type: "POST",
url: jsonUrl,
contentType: 'application/json; charset=utf-8',
dataType: 'json',
traditional: true,
data: JSON.stringify({
Values: chiavi
}),
success: function (result) {
},
error: function (response, textStatus, errorThrown) {
}
});