This is a character-by-character beginner course in Chinese, provided free of charge at the Open Languages Project. It teaches you to read (and listen to) Chinese by explaining and introducing one character at the time, including dialogues based on the characters you have learnt so far. While not perfect and occasionally incorrect, it's still the best such attempt I can think of. The audio is also okay with decent and fairly natural recording.

From their own introduction:

In this course, we will teach you how to read at the same time as we teach you how to understand the language. We teach only one character at a time, with constant revision to help you remember them. The romanised form (Pinyin) is used only with the introduction of the character, then you need to remember the sound each character represents as it is used in various sentences and dialogues. There are flash cards at the end of every 20 lessons to help you.