Fitting distribution - Chi Square Test

I'm need to test some data for my masterthesis. I'm a newbie to statistics, so please forgive any stupid errors I may have done. I use R for all calculations. I have set of 900000 discrete data points in the range from 1 to 600. I wanna fit a distribution to that data set. I think it is a poisson distribution with overdispersation. As result of that I choose this theoretic distribution: rnbinom(length(data), size=mean(data)/(var(data)/mean(data))-1, mu=mean(data))

I performed some visual test to see if this distributions might be reasonable. I created a plot with real data and the theoretic data and watched if they match. The other thing I did was a qqplot. Both test seems ok.

Then I performed a chi square test with the data sets. I repeated the test with different "pulls" of the distribution. The p-value toggles between 1 and almost 0. I don't know what to do with this result. Does it help to use the monte-carlo option of the test?