Can hydrocarbons undergo combustion without oxygen present?

Most of us are familiar with the standard reaction of methane gas combustion:

$$\ce{CH4 + 2O2 -> CO2 + 2 H2O}$$

In standard combustion, oxygen is generally used as the oxidant. Would it be possible for hydrocarbons to undergo combustion using alternative oxidants? If so, under what conditions could this be reproduced?

For example, could we achieve anoxic combustion by replacing oxygen in the atmosphere with another highly electronegative element such as chlorine or fluorine? Or perhaps compounds in high oxidation states such as permanganate or dichromate under different pressure/temperature conditions such that they were gaseous?

• Note that permanganates and dichromates both contain oxygen. – Todd Minehardt Mar 13 '17 at 20:19
• This Q&A discusses, among other things, how a combustion engine could work in a Cl2/Ar atmosphere. Nothing about this is good for humans, but just from a perspective of chemical curiosity, sure you could do it. Since Earth doesn't have an appreciable amount of Cl2 in the air, you would have to carry around both oxidant (Cl2) and reductant (hydrocarbon). Then, in the simplest case of methane, I suppose your exhaust would be carbon tet and HCl. No thanks ;) – airhuff Mar 13 '17 at 22:44

They would certainly combust if meeting a worse adversary than oxygen. $\ce{ClF3}$ would oxidize them, with extreme certainty, rapidity and violence.
Here is a short excerpt from the Wikipedia article of $\ce{ClF3}$ which amused me: