At the beginning of Parshat Lekh Lekha, G-d commands Avraham: "Lekh Lekha - Go away from your land, from your birthplace, and from your father's house, to the land that I will show you. I will make you into a great nation?" (Bereishit 12:1-2)
Why does G-d choose Avraham? Although Avraham's greatness becomes manifest in later chapters of the Torah, at this stage of the biblical narrative we know virtually nothing about him; we have a little background about his family tree and that's it. This dearth of information stands in sharp contrast to the depiction of the previous hero of the Bible, Noach, whose character traits and worthiness are described before he is chosen.
The Sfat Emet, basing himself on the Zohar, explains that the fact that Avraham listened to the command of Lekh Lekha, in and of itself displays his distinction. According to the Sfat Emet, G-d's message, his "Lekh Lekha", was available to everyone, all the time, but since they did not make any effort to hear the Divine revelation it was is as if they were sleeping. Only Avraham made the effort to hear G-d's words. Ultimately, it was as if G-d spoke only to Avraham, because only Avraham was attuned and waiting to hear Him.
Thus, we can answer our question of "Why does G-d choose Avraham?" by saying that G-d chose Avraham because Avraham chose G-d.
Shabbat Shalom!