I believe they do. But I think I've heard they also start with the age of 1, rounding up and counting the 9 months spent in the womb.

Here is some interesting information: Traditionally, Chinese people do not pay a lot of attention to birthdays until they are 60 years old. The 60th birthday is regarded as a very important point of life and therefore there is often a big celebration. After that, a birthday celebration is held every ten years, that is the 70th, the 80th, etc, until the person's death. Generally, the older the person is, the greater the celebration occasion is. The Chinese traditional way to count the age is different from the Western way. In China, people take the first day of the Chinese New Year in lunar calendar as the starting point of a new age. No matter in which month a child is born, he is one year old, and one more year is added to his age as soon as he enters the New Year. So what may puzzle a Westerner is that a child is two years old when he is actually two days or two hours old. This is possible when the child is born on the last day or hour of the past year. It is often the grownup sons and daughters who celebrate their elderly parents' birthdays to show their respect for them and express their thanks for what they have done for their children. According to the traditional customs, the parents are offered foods with happy symbolic implications. On the birthday morning the father or mother will eat a bowl of long "long-life noodles." In China long noodles symbolize a long life. Eggs are also among the best choices of food taken on the special occasion. To make the occasion grand, other relatives and friends are invited to the celebration. In Chinese culture, 60 years makes a cycle of a life and 61 is regarded as the beginning of a new life cycle. When one is 60 years old, he is expected to have a big family filled with children and grandchildren. It is an age to be proud of. That's why elderly people start to celebrate their birthdays at 60. Regardless of the scale of the celebration, peaches and noodles, which are both signs of long life, are required. But interestingly the peaches are not real. They are actually steamed wheaten food with sweet stuff inside. They are called peaches just because they are made in the shape of peaches. When the noodles are cooked, they should not be cut short, for the shortened noodles can have a bad implication. Everyone at the celebration eats the two foods to extend their best wishes to the long-life star. The typical birthday presents are usually two or four of eggs, long noodles, artificial peaches, tonics, wine and money in red paper. http://chineseculture.about.com/library/weekly/aa021901b.htm

Here is some interesting information: Traditionally, Chinese people do not pay a lot of attention to birthdays until they are 60 years old. The 60th birthday is regarded as a very important point of life and therefore there is often a big celebration. After that, a birthday celebration is held every ten years, that is the 70th, the 80th, etc, until the person's death. Generally, the older the person is, the greater the celebration occasion is. The Chinese traditional way to count the age is different from the Western way. In China, people take the first day of the Chinese New Year in lunar calendar as the starting point of a new age. No matter in which month a child is born, he is one year old, and one more year is added to his age as soon as he enters the New Year. So what may puzzle a Westerner is that a child is two years old when he is actually two days or two hours old. This is possible when the child is born on the last day or hour of the past year. It is often the grownup sons and daughters who celebrate their elderly parents' birthdays to show their respect for them and express their thanks for what they have done for their children. According to the traditional customs, the parents are offered foods with happy symbolic implications. On the birthday morning the father or mother will eat a bowl of long "long-life noodles." In China long noodles symbolize a long life. Eggs are also among the best choices of food taken on the special occasion. To make the occasion grand, other relatives and friends are invited to the celebration. In Chinese culture, 60 years makes a cycle of a life and 61 is regarded as the beginning of a new life cycle. When one is 60 years old, he is expected to have a big family filled with children and grandchildren. It is an age to be proud of. That's why elderly people start to celebrate their birthdays at 60. Regardless of the scale of the celebration, peaches and noodles, which are both signs of long life, are required. But interestingly the peaches are not real. They are actually steamed wheaten food with sweet stuff inside. They are called peaches just because they are made in the shape of peaches. When the noodles are cooked, they should not be cut short, for the shortened noodles can have a bad implication. Everyone at the celebration eats the two foods to extend their best wishes to the long-life star. The typical birthday presents are usually two or four of eggs, long noodles, artificial peaches, tonics, wine and money in red paper. http://chineseculture.about.com/library/weekly/aa021901b.htm

i'm chinese, and the way this works is that yes, you do celebrate your own birthday and you do officially turn a year older on that day. but your actual birth age is what we call, quite literally translated, "real age". the fact that another birthday is celebrated on new year's (note chinese new year not january 1st) gives every person a "fake age" or "feint age". the feint age is always one year older than the person's actual age. for example, if someone turns 14 on their actual birthday, their fake age will become 15 once the next new year's comes. legally, chinese people's ages are recorded according to "real age". socially and culturally, a person's age is their "fake age". this goes especially for younger adults and below. so if someone were to ask casually a 12-year-old what their age was, the proper reply would be 13 because it is assumed that is the "feint age".