We arrive at Heathrow, from Chicago, at 6:00 am on a Friday (September). Is it necessary to purchase train tickets from St Pancras to Paris in advance, or can we wait and purchase our tickets when we arrive at St Pancras?
Always purchase Eurostar tickets in advance. The cheapest tickets sell out first, and September tickets are on sale now.
You can purchase Chunnel train tickets at the station on the day of your journey, but you will be paying the highest fare. Chunnel uses airline style pricing so the sooner you purchase the cheaper it will be: http://tinyurl.com/chunnel-train
If you want a cheap ticket, go to www.eurostar.com and book ASAP. I would warn you, however, that the cheap tickets are strictly tied to a single train and (almost uniquely for European trains) there's a half-hour check-in deadline, so if your flight is delayed or your journey from the airport is disrupted you will have to pay a new full-price fare. I'd suggest that if you want to get a cheap ticket you book for an afternoon departure and spend a couple of hours sightseeing in London if you're on time. (The British Library is next door to the station and the British Museum is a short bus or tube ride away.)
You will need to allow up to one hour to clear immigration/passport control, just over one hour to take the Tube (Piccadilly Line) from Heathrow to King's Cross/St Pancras, and up to one hour to make sure you meet the 30-minute check-in deadline. I would add a minimum of two more hours to allow for the possibility of a flight delay.
Perhaps you've cosnidered this and discounted it, but as you are already at Heathrow why not fly to Paris? If you get your tickets connected you can make an airside connection and avoid UK immigration. You also avoid the trip into London (though I accept that is balanced out by the need to get into central Paris at the other end). BA fly several times each day on that route - I imagine Air France do too.
Thanks for the very helpful feedback.
Despite a misinformation campaign on the Helpline to encourage use of the term <chunnel> it is a term not used. You will be best served by using the correct term of Eurostar. If you use the other you will be marked out as an unknowing hick by most Londoners or Parisiens, and many people won't know what you are talking about. That being said, I agree that is you are at Heathrow already you would probably be well served by grabbing a puddle jumper over the water to Paris. Say the plane's an hour late, 0700 arrival. 0800 through baggage claim, unless you have carryon only. If you don't have anything but carryon you could be heading to Paris by 0900 or 1000. You'd be in the centre of Paris by lunchtime. If you use the Eurostar with nable tickets and a minimum 30 minute check in, you are looking at 0800 start to find the Underground at Heathrow, 0930 arrival at check in at Eurostar. The first reasonably safe departure would be at 1025 with arrival at Paris Gare du Nord at 1347. An even safer one would be 1225 to 1547. If you could organize an easy transfer at Heathrow, especially on the same ticket which would guarantee the connection, that's what I would do.
We did the London-Paris train after arriving at Heathrow around 6-7am. I honestly can't remember if we bought our tickets ahead (it was 2010 - 3 yrs is a long time for me...ok, hubby says when we got there, not in advance, it was mid-Sept, and I think we had a train for around 10am, I know we got into Pris early afternoon). We went into St Pancras and ate some breakfast...got on the train...and both pretty much fell asleep for the whole journey. I remember about 20 min outside of London, a glimpse of some farmer's fields thru half closed eyes, and then about 10min before Paris. Hubby remembers a bit more, but not much. Hindsight - it probably would have been better (and cheaper since we didn't buy in advance) to hop a flight while we were in the airport. I just hope I wasn't drooling/snoring the whole way, and am really glad no one decided to make off with our bags!
You can use Kayak.com to find cheap flights in Europe if you can't fly direct to Paris. We used it to find amazingly cheap flights for Berlin to Copenhagen, Copenhagen to Amsterdam, Vienna to London, London to Amsterdam. We have heard the term "Chunnel" used in the UK, but only for the physical tunnel itself. We agree Eurostar is the correct term for the train. We also don't use it anymore as the trip is expensive and so boring you fall asleep (big ditch in ground, tunnel with no lights, big ditch in ground interrupted by trains going the other way so fast & close it scares the blank out of you the first time). We only saw the Channel for about 10 seconds as we went into the tunnel.