European Rail Travel - Chisinau - Odessa train

I know there is a direct train between Chisinau and Odessa. Has everyone ever taken it? How was it? Price? And the border crossing for and EU member, easy? Does it go through Pridnestrovian?

And how about Chisinau? Is the city safe?

Thanks for the help!

Here's a page with some info that seems to be pretty up-to-date:

http://www.marisha.net/crossroads.htm#odessa

I took the train last November. I was planning a trip to eastern Europe and had read that the Transdnistrians had recently given up their silly harassing of passengers passing through Transdnistria (they had been extorting "visa fees" of $30 or 20 Euros or whatever the traffic woud bear). I was in Odessa (a wonderful city, highly recommended) and wanted to go to Chisinau and Bucharest, so I bought a ticket in Odessa to Chisinau (ridiculously cheap). The train left in the late afternoon; it was a Moldovan local-traffic train, pulled by a diesel engine, not an elektrishka, as the next posting's link claims - Chisinau has no electric train service) and I seemed to be the only non-Ukrainian or -Moldovan on board. Some Moldovans who spoke English chatted with me, so the trip was quite pleasant. I don't recall any stop in Pridnestrovian, which also is not shown on the DB-hafas itinerary of the train; it did stop in Tiraspol (in Transdnistria), however. The Ukrainians checked and stamped passports on the border, but the Transdnistrians never showed up. The Moldovans came through the train after we had passed the Transdnistrian/rest-of-Moldovan border and just glanced at my passport (U.S.). This was a mistake, as the Romanians were quite put out that I didn't have a Moldovan stamp in my passport, but once I showed them my Odessa-Chisinau train ticket, they stamped my passport and let me enter Romania (in a sleeper on the overnight Chisinau-Bucharest train). Chisinau was surprisingly attractive and interesting. It's a cultivated, busy city with an opera house (on Maria Cebotari St., of course) and decent restaurants. The hotel was even quite good. I think that EU citizens would have an equally easy time on the train and in Moldova (it wants to join the European Union, after all). Go!