Also bear in mind that
Onefactor anova is "a generalization of the
twosample ttest." The 2sample ttest can deal with unequal variances, which leads me to think that so can ANOVA.
Quote by Engineering Stat. Handbook, sec. 1.3.5.3 (TwoSample tTest for Equal Means)
The variances of the two samples may be assumed to be equal or unequal. Equal variances yields somewhat simpler formulas, although with computers this is no longer a significant issue.

But, a particular software package may not have this option. In some ANOVA packages (like SAS) specifying the "Welch" option controls for unequal variances.