Constant or variable number of chiasmata during recombination?
There is a large amount of variation in the distribution and number of chiasmata or crossing overs (COs). The total number of chiasmata per cell can vary within the same organism.
Where chiasmata occur along the chromosome is also not consistent cell to cell. Hotspots are 1-2kb regions that experience elevated recombination compared to neighboring genomic regions. A way to think of the distribution of COs is that ~80% of recombination happens in hotspots which comprise ~10% of the genome.

Recombination depends on the chromatin context, so chiasmata are rare near the centromere and positive interference results in chiasmata being spaced out along the chromosome. A good prediction of total chiasmata number per cell is at least 1 per chromosome. Some researchers argue that one CO per chromosome arm is more accurate. 

Below is a link to a good article that expands on some of the ways recombination varies in humans.
http://www.nature.com/nrg/journal/v8/n1/abs/nrg1947.html