What is the cost of an endowed chair in a medical school? What would be a typical cost for a donor to start up an endowed chair for a professor (an MD) in a medical school?  Are there ongoing costs?
For a fully endowed position, multiply the expected salary, benefits, and research funds by 20x to get an approximation. 

If the researcher is making $250,000 in salary and benefits and $250,000 in funding for their lab, then you would want around $10,000,000 endowment minimum (salary and lab numbers chosen for ease of calculation rather than proximity to reality). 

This assumes a 5% per annum draw on the endowment, which is both conservative and average. A university with better fund managers could draw 8-10%; a very conservative institution or a place that wants to grow the endowment endogenously might only draw 3-5%.  

And as @Dawn notes, for some positions not all position costs are paid entirely out of the endowment, and thus may require a smaller investment. For example, some endowed chairs might only receive 30% of their salary from the named endowment and the rest from general funds. If that were the case in the above example, the endowment would only have to be at the $3 million level.