Answer:
   
   Contrary to popular belief, nowhere in the Tanakh [Hebrew Bible] or in
   classical Jewish literature is there a claim that Jews are G-d's only
   "chosen people". The closest that one finds is Exodus 19:5, which
   states that Jews are an "am segulah", a "treasured people", but this
   is a very different claim indeed. The misunderstanding on this issue
   stems from the fact that most people are unfamiliar with the claims
   that Judaism actually makes in regards to chosenness. So what does
   classical Judaism actually state? Consider the bracha [blessing] said
   before reciting the Torah: Praised are you, Lord our G-d, King of the
   universe, who has chosen us out of all the nations to bestow upon us
   His Torah.
   
   Also consider the blessing recited as an introduction to the reading
   of the "Shema Yisrael" the selection of verses from the Torah
   (especially Deuteronomy 6:4-8) that proclaim the sovereignty of G-d
   and our commitment to his Torah. The blessing relates to the act of
   the recitation as a fulfilment of the religious obligation of Torah
   study. You have loved us with abounding love, O Lord our G-d, you have
   shown us great and overflowing tenderness. For the sake of our
   ancestors who trusted in you, and whom you instructed in the precepts
   of life - in the same manner, be gracious unto us and instruct us...
   Put it into our hearts to understand, to become wise, to hear, to
   learn, to teach, to observe, to do, to uphold - all the words of the
   study of Torah, lovingly... For you are the performer of wonders, and
   you have chosen us out of all nations and tongues, and brought us
   close to your great name in truth... Blessed are you, Lord, who
   chooses His people Israel in love.
   
   The relationship between G-d and the Jewish people is summed up when
   He calls us in the book of Exodus as "my son, my eldest, Israel". We
   are not firstborn in any literal sense, see the geneologies in the
   begining of Genesis. However, your eldest child is the one you leave
   the most responsibility and the most reward to. (Assuming they live up
   to that responsibility.)
   
   The key notion is that there is no thing called the "chosen people,"
   but rather that "choosing" is invariably perceived as a verb. It is a
   dynamic activity that is inextricably identified with Israel's devoted
   observance of the precepts of the Torah. Rather, there are people whom
   G-d has sanctified by commanding them to rest on the Sabbath, to
   rejoice in the festivals, to study the Torah and to accept the yoke of
   G-d's supremacy over all other allegiances. It certainly has nothing
   to do with any claim of superiority. In fact, the prophet Amos (3:2)
   states the opposite: "You alone have I singled out of all the families
   of the Earth, that is why I will call you to account for your
   iniquities". Other nations can fulfill G-d's will with only [5]seven
   commandments, rather than the hundreds required of Jews. The concept
   in fact is "chosen to fulfill a responsibility," and implies a harder
   task rather than a higher status in the world.
   
   Finally, note that there is no claim to exclusivity in the regards of
   love from G-d, nor in regard to being able to be chosen for a
   particular purpose. There is only the claim that we were chosen to
   bring the biblical message of the prophets, and to cleave to Torah as
   a way of life. Judaism has always affirmed that gentiles can have a
   close relationship with G-d as well, and perhaps other nations are
   chosen for their own purposes as well.