According to Deuteronomy 7:6, the Israelites are called the "chosen people". Who in fact are the chosen people, and does this include Christians?
What sets the chosen people apart, are there special rights or honors that go with this title?
The "chosen people" are, as you mention the Israelites.
This simply means that God has chosen these people and set them aside to be holy.
It all began with Abraham:
That was the original "chosing", if you will. After that came Isaac and Jacob, who was called Israel.
With Israel (Jacob), God renewed the blessing above (in Genesis 28), saying specifically (in that passage):
A man becomes a nation (more history)
God was faithful to his promise to Abraham and Jacob. He made a great nation out of the Israelites and turned them into a nation while they were enslaved in Egypt.
When he freed them from Egypt, he lead them to the base of a mountain and established a few ground rules (the 10 commandments). Later (not much later), he established an entire set of rules that can be found in Leviticus.
These set of rules were the original covenant. The essence of it can be seen in Leviticus 26, but it basically says:
Summary (What it means to be chosen)
God set the nation of Israel aside. They would be his people and he would be their God.
If they followed him, they would be blessed. If they turned from him, they would be cursed.
Christians are not the Israelites. Christians are not the "chosen people".
Christians are chosen
Having said that, Christians are, undoubtedly, chosen (although we are not "The Chosen People").
If you read through that, what you'll see is that Jesus has set us aside and given us the same type of covenant that you see mirrored in Leviticus (and Deuteronomy, for that matter). Specifically:
He goes on to say that he will be part of us and we will be part of him. Clearly, we are "chosen" in this sense.
Christians are "chosen". This means we live in Jesus and we are a part of Jesus and we will inherit eternal life. He has chosen us for eternal life. However, we are not the "chosen people". (See the first half of this answer for that.)