Can InStat or Prism compare observed and expected counts (frequencies) with a chi-square test? (I don't want to analyze a contingency table, I want to enter the observed and expected values for each category.)

InStat cannot compare observed and expected counts with a chi-square test. Neither can Prism up to version 5. However, Prism 6 can do this calculation. Enter the observed distribution on the new parts-of-whole table and the choose the new analysis. Additionally, we have created a free web calculator that does this calculation. Try it.