Hi James,
Judaism teaches that all nations have been chosen by G-d to follow the destiny set out for each. Therefore when one reads that the Jews were "chosen" by G-d, it means "chosen" in reference to their specific destiny. It does not make us any more special than others. Even nations that worshipped heathen gods still bring their "piece of the puzzle" that makes society work and beneficial for all. All different nations and ethnic groups actually rely on one another, and peace is actually when each follows through with whatever they are supposed to be doing and when others allow them the freedom to do this.
Christianity might have been responsible for changing the "chosen" interpretation to "special." In their eyes they have replaced the Jews as G-d's people (where as in Judaism all humans are G-d's people), interpreting Hebrew Scripture texts in such as way as to make them, Christians, sound as if they were more enlightened, more essential, and in some way therefore more important to the history of humankind. (As a consequence this idea that this is how Jews also feel about themselves often gets mistakenly transferred to us.) Christians have even given this economy a theological name: "salvation history." Whereas the Jews see themselves as being saved by G-d, Christians turned this around to make them sound as the "chosen people" assigned to save the world through the preaching of the Gospel.
Now if you mean by your question, do Jews still see themselves in a covenant relationship with G-d? The answer would be "yes." However we also understand the Law of Moses as something that is fluid with the changing needs of G-d's people, so how we respond to G-d today through Torah observance differs from the way it was carried out centuries ago.
Lastly you might find it interesting to note that Jews take an approach to G-d more in line with atheism than one like Christianity. Belief in G-d is not as important as how one brings G-d into the world. One line of thought is for Jews to act as if there is no G-d, and therefore to act as G-d for the world. This means not teaching others to worship according to some creed but caring for the world and for people as G-d would "in G-d's absence," so to speak. Instead of debating over the existence or nature of G-d, Jews get up and do something to help the world. In that way they are "chosen" to be G-d for a world without one.