Film a wide pan with the oil and get it hot. Venison is lean enough that it will not render anything to cook in, so the oil is doing the job the fat would do in beef.
Brown the venison in two batches so it is never crowded, letting each batch sit untouched before you break it up. It will spit and go grey and wet first. Keep going. When the spitting stops and the sizzle turns sharp and dry, the crumbles start catching brown. That sound is the water leaving, and nothing browns until it has.
Onion in, 3 minutes, until it loses its bite. Garlic for the last minute only. The pan has been driven hot to brown lean meat and garlic scorches in about two.
Tomato paste in, 2 minutes without moving it much, until it darkens and smells sweet rather than raw.
Tomatoes, stock, cumin, chili powder, smoked paprika and cayenne. Stir and bring to a low simmer.
Simmer uncovered 30 to 45 minutes, until a spoon dragged across the bottom leaves a track that stays open for a second before the chili closes over it. Venison is lean enough that no fat will ever rise to the top, so do not wait for it. If it is still loose, keep going with the lid off. Salt to taste at the end.