In a rather odd reversal of known science, the latest chemtrail theory is that modern high-bypass engines do not create contrails. A comprehensive explanation of why this is incorrect can be found in the following video:
As noted towards the end of the video, the idea can be debunked simply by a review of the scientific literature. The likelyhood that a particular engine will create a contrail is governed by the "contrail factor", and this is higher for high bypass engines - I encourage you to research this for yourself, and I give some links below.
The classic demonstration of high bypass engines producing more contrails is the study:
Ulrich Schumann and Reinhold Busen, 2000, Experimental Test of the Influence of Propulsion Efficiency on Contrail Formation
As you can see, the newer high-bypass A340 produces contrails more frequently than the older, low-bypass B707
Schrader, Mark L., 1997: Calculations of Aircraft Contrail Formation Critical Temperatures. J. Appl. Meteor., 36, 1725–1729.
Fig 4 shows contrails forming at a wider range of temperatures than non or low-bypass engines. You don't have to follow exactly what the graphs mean, just note that for the high-bypass engine, the curves intersect the bottom axis at a higher temperature than the low-bypass or non-bypass engines.
Walters, Michael K., Jeffrey D. Shull, Robert P. Asbury, 2000: A Comparison of Exhaust Condensation Trail Forecast Algorithms at Low Relative Humidity. J. Appl. Meteor., 39, 80–91.
Influence of propulsion efficiency on contrail formation Ulrich Schumann
Lynch, David K., et al, 2002: Cirrus, Oxford University Press
http://books.google.com/books?id=58v1fg4xeo8C&lpg=PA233&ots=_-uNkL6yUM&dq=contrail factor high bypass&pg=PA233#v=onepage&q&f=false
So what did the theorists get wrong?
This theory is particularly odd in the context of the chemtrail theory, as that normally claims that in previous decades (generally the 1980s and before) there were no persistent contrails, and that the contrails we see now are something new. But this new spin on the chemtrail theory seems to be arguing the opposite - that older planes would make contrails, and new planes will not.
The thinking behind the "high-bypass = no contrails" seems to be the idea that the contrail is made from the air that an engine pushes backwards. This is incorrect - simply pushing air does not create an exhaust contrail. An exhaust contrail is created from, as the name implies, the exhaust of the the engine.
The exhaust of the engine is the gasses that come out of the combustion chamber. It's the product of burning kerosene (hydrogen and carbon) with the oxygen in the air, and the result is carbon dioxide and dihydrogen monoxide (water). It's the water in the exhaust that makes the contrail. And the exhaust gasses are basically the same regardless of if it's a low-bypass, no-bypass, high-bypass or even an internal combustion engine.
What creates a contrail is the mixing of the exhaust with cooler air. It does not matter if it's mixing with the air that passed through the bypass fan, or if it's mixing with the air that passed around the engine. It's still just exhaust gases mixing with the air. As the gasses mix, the temperature falls, and the water condenses out.
The only difference with a high bypass engine is that the exhaust gasses in a high bypass engine are a little less hot (more of the energy has gone into producing thrust from the bypass fan). So they reach the condensation point quicker, and so are more likely to form contrails.
In reality, any plane can make a contrail. High bypass, low bypass, no bypass, even prop planes will make contrails. And they always have.