I'm confused as well regarding the recommendation for a chi-square test on HB utilities for CBC experiments. Perhaps you can ask your supervisor for a clarification?
The only connection I could see to Chi-Square is through the log-likelihood fit resulting from the multinomial level model involved in HB. Twice the log-likelihood is distributed Chi-Square. But, we have LL for each respondent. So, for each LL there is a Chi-square test comparing it to the null LL (likelihood resulting from utilities of zero). Given what I know about HB and resulting LL fit, most respondents will pass the threshold of 95% confidence (significantly different from utilities of zero).
For example, if there are 4 alternatives per choice task, then the null fit is ln(1/4) for each choice task. We add that across choice tasks within the respondent to calculate total LL for the null model for the respondent. We could then calculate the likelihood of the chosen tasks for the respondent according to the logit equation. We could add the natural logs of the likelihoods across tasks for these predicted likelihoods given the HB utilities. Degrees of freedom would be the number of estimated parameters in the model. BTW, Sawtooth Software won't calculate these statistics I'm referring to at the individual level from HB.