It is very important to use the word "Christian" with care here. While it is true that Roman Catholic Church did a lot in the past to hinder scientific advancement, we must remember that it doesn't represent Christian Church in a biblical sense.
During the dark ages misinterpretation of Scriptures did much harm to scientists who redefined the understanding of our solar system among whom were Nickolaus Copernicus and Galileo, the latter of whom had to pay with his life for scientific discoveries that became our common knowledge.
Nevertheless, these scientist were not atheists, as a matter of fact many scientists that would follow did not hide their belief in God. Issac Newton, for example, used the Bible as inspiration for his scientific studies.
There is nothing in the Scriptures that would forbid acquiring scientific knowledge, on the contrary, it holds it in very high esteem by declaring that the entire universe proclaims the glory of God. There is nothing in them that suggests the earth to be in the center of the universe, as Roman Catholic Church firmly believed, but it mentions the "circle of the earth", and talks about stars and planets following a "path", or in our modern language an orbit.
Consider curious statement made by apostle Paul, "Things which are seen are made of the things unseen...,"thanks to the quantum physics today and modern technology, we know that there are particles of matter that are not visible to the naked human eye, and this makes the apostle's statement to be very accurate.
The only points in which the Christian church and majority of scientific body disagree are the theory of evolution, ethical issues pertaining to mixing human DNA with that of animals, and using human embryo for stem cell research.
The theory of evolution is still just a theory, which by the way, may even hinder scientific progress if it becomes a dogma that would disqualify any new approaches to explaining the world around us just because they don't fit this theory.
Mixing human DNA with that of animals might cause unexpected side effects just as it did with genetically mixed fruit and vegetables that we found out are not so healthy after all.
And as for using human embryo in stem cell research, the latest findings suggest that skin cell might work for it as good or even better from that of the embryo.
So, how Christian church hindered science? All things considered, my answer is that it didn't hinder it at all.