Is chi-squared always a one-sided test? A published article (pdf) contains these 2 sentences:

Moreover, misreporting may be caused by the application of incorrect rules or by a lack of knowledge of the statistical test. For example, the total df in an ANOVA may be taken to be the error df in the reporting of an $F$ test, or the researcher may divide the reported p value of a $\chi^2$ or $F$ test by two, in order to obtain a one-sided $p$ value, whereas the $p$ value of a $\chi^2$ or $F$ test is already a one-sided test. 

Why might they have said that?  The chi-squared test is a two-sided test.  (I have asked one of the authors, but gotten no response.)
Am I overlooking something?
 A: The chi-square test $(n-1)s^2/\sigma^2$ of the hypothesis that the variance is $\sigma^2$ can be either one- or two-tailed in exactly the same sense that the t-test $(m-\mu)\sqrt{n}/s$ of the hypothesis that the mean is $\mu$ can be either one- or two-tailed.
A: The chi-squared test is essentially always a one-sided test.  Here is a loose way to think about it: the chi-squared test is basically a 'goodness of fit' test.  Sometimes it is explicitly referred to as such, but even when it's not, it is still often in essence a goodness of fit.  For example, the chi-squared test of independence on a 2 x 2 frequency table is (sort of) a test of goodness of fit of the first row (column) to the distribution specified by the second row (column), and vice versa, simultaneously.  Thus, when the realized chi-squared value is way out on the right tail of it's distribution, it indicates a poor fit, and if it is far enough, relative to some pre-specified threshold, we might conclude that it is so poor that we don't believe the data are from that reference distribution.
If we were to use the chi-squared test as a two-sided test, we would also be worried if the statistic were too far into the left side of the chi-squared distribution.  This would mean that we are worried the fit might be too good.  This is simply not something we are typically worried about.  (As a historical side-note, this is related to the controversy of whether Mendel fudged his data.  The idea was that his data were too good to be true.  See here for more info if you're curious.)
A: 
Is chi-squared always a one-sided test?

That really depends on two things:


*

*what hypothesis is being tested. If you're testing variance of normal data against a specified value, it's quite possible to be dealing with the upper or lower tails of the chi-square (one-tailed), or both tails of the distribution. We have to remember that $\frac{(O-E)^2} E$ type statistics are not the only chi-square tests in town!

*whether people are talking about the alternative hypothesis being one- or two-sided (because some people use 'two-tailed' to refer to a two-sided alternative, irrespective of what happens with the sampling distribution of the statistic. This can sometimes be confusing. So for example, if we're looking at a two-sample proportions test, someone might in the null write that the two proportions are equal and in the alternative write that $\pi_1 \neq \pi_2$ and then speak of it as 'two-tailed', but test it using a chi-square rather than a z-test, and so only look at the upper tail of the distribution of the test statistic (so it's two tailed in terms of the distribution of the difference in sample proportions, but one tailed in terms of the distribution of the chi-square statistic obtained from that -- in much the same way that if you make your t-test statistc $|T|$, you're only looking at one tail in the distribution of $|T|$).
Which is to say, we have to be very careful about what we mean to cover by the use of 'chi-square test' and precise about what we mean when we say 'one-tailed' vs 'two-tailed'.
In some circumstances (two I mentioned; there may be more), it may make perfect sense to call it two-tailed, or it may be reasonable to call it two-tailed if you accept some looseness of the use of terminology. 
It may be a reasonable statement to say it's only ever one-tailed if you restrict discussion to particular kinds of chi-square tests. 
A: I also have had some problems to come to grips with this question as well, but after some experimentation it seemed as if my problem was simply in how the tests are named. 
In SPSS as an example, a 2x2 table can have an addition of a chisquare-test. There there are two columns for p-values, one for the "Pearson Chi-Sqare", "Continuity Correction" etc, and another pair of columns for Fisher's exact test where there are one column for a 2-sided test and another for a 1-sided test.
I first thought the 1- and 2-sides denoted a 1- or 2-sided version of the chisquare test, which seemed odd. It turned out however that this denotes the underlying formulation of the alternate hypothesis in the test of a difference between proportions, i e the z-test. So the often reasonable 2-sided test of proportions is achieved in SPSS with the chisquare test, where the chisquare measure is compared with a value in the (1-sided) upper tail of the distribution. Guess this is what other responses to the original question already have pointed out, but it took me some time to realize just that.
By the way, the same kind of formulation is used in openepi.com and possibly other systems as well. 
A: @gung's answer is correct and is the way discussion of $\chi^2$ should be read. However, confusion may arise from another reading:
It would be easy to interpret a $\chi^2$ as 'two-sided' in the sense that the test statistic is typically composed of a sum of squared differences from both sides of an original distribution.
This reading would be to confuse how the test statistic was generated with which tails of the test statistic are being looked at.
A: $\chi^2$ test of variance can be one or two sided: The test statistic is $(n-1)\frac{s^2}{\sigma^2}$, and the null hypothesis is: s (sample deviation)= $\sigma$ (a reference value). The alternative hypothesis could be: (a) $ s> \sigma$, (b) $s < \sigma$, (c) $s \neq \sigma$. p-value caculation involves the asymmetry of the distribution.
A: The $\chi^2$ and F tests are one sided tests because we never have negative values of $\chi^2$ and F. For $\chi^2$, the sum of the difference of observed and expected squared is divided by the expected ( a proportion), thus chi-square is always a positive number or it may be close to zero on the right side when there is no difference. Thus, this test is always a right sided one-sided test. The explanation for F test is similar.
For the F test, we compare between group variance to sum of within group variances ( mean square error to $\frac{SSw}{dfw}$. If the between and within mean sum of squares are equal we get an F value of 1. 
Since it is essentially the ratio of sum of squares, the value never becomes a negative number. Thus, we don't have a left sided test and F test is always a right sided one sided test. Check the figures of $\chi^2$ and F distributions, they are always positive.For both tests, you are looking at whether the calculated statistic lies to the right of the critical value.   

