Box-Cox data transformation to enable linear regression

Box-Cox transformation works fine with zeros. Hope you are using boxcox.fit() in package named geoR.

However, you can solve your problem of skewness with other transformations like:

1. Square root transformation. However, often the square root is not a strong enough transformation to deal with the high levels of skewness.
2. Use log(x+1) transformation which is a widely accepted way of feature transformation.

Also, I don't understand why you are doing transformation of the dependent variable. I agree with @dave for the assumption of normality in regression.