Is there a group of Jews today who still believe they are God's chosen people?
As best that I can tell, most, if not all, in the Jewish faith believe that they are God's chosen people. There are variations on exactly what is meant by being the chosen people, but I have found that Jews are united in the belief that they have not and will not be un-chosen by God.
What they willfully ignore is God's condition on their being His people. "Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure to Me above all people; for all the earth is Mine" (Exodus 19:5). God did not offer a permanent, unconditional election. Nor did God state that only the Israelites alone would remain chosen. "Then I will sow her for Myself in the earth, and I will have mercy on her who had not obtained mercy; then I will say to those who were not My people, 'You are My people!' And they shall say, 'You are my God!'" (Hosea 2:23). Paul refers to this as proof that God accepted the Gentiles. "As He says also in Hosea: "I will call them My people, who were not My people, And her beloved, who was not beloved. And it shall come to pass in the place where it was said to them, 'You are not My people,' There they shall be called sons of the living God." ... What shall we say then? That Gentiles, who did not pursue righteousness, have attained to righteousness, even the righteousness of faith; but Israel, pursuing the law of righteousness, has not attained to the law of righteousness. Why? Because they did not seek it by faith, but as it were, by the works of the law. For they stumbled at that stumbling stone" (Romans 9:25-26, 30-32). Peter also refers to the same prophecy when speaking to Christians, "But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light; who once were not a people but are now the people of God, who had not obtained mercy but now have obtained mercy" (I Peter 2:9-10).
God's chosen people today are Christians. Both Jews and Greeks can be a part of His kingdom, but there is no salvation outside of it.