Nope nope nopity nope. E-fences are problematic on so many levels, not least the electric shock. If she's chasing something and goes across it, there's a better than good chance she'll be too afraid to cross it to come back in. And it ain't going to keep any critters out that can harm her, or that she'll chase. Here's a really good article, based in academic research, which lays out the pros and cons really well. http://dogtime.com/dog-health/genera...e-podolsky-faq
(Can't you even fence off a little piece of it? Doesn't have to be anything permanent...my fence is just that wire garden edging with chicken wire strung along it. Works just fine.)