Transformer-based models trained on large and general purpose datasets consisting of molecular strings have recently emerged as a powerful tool for successfully modeling various structure-property relations. Inspired by this success, we extend the paradigm of training chemical language transformers on large-scale chemical datasets to generative tasks in this work. Specifically, we propose GP-MoLFormer, an autoregressive molecular string generator that is trained on more than 1.1B (billion) chemical SMILES. GP-MoLFformer uses a 46.8M parameter transformer decoder model with linear attention and rotary positional encodings as the base architecture. GP-MoLFormer's utility is evaluated and compared with that of existing baselines on three different tasks: \textit{de novo} generation, scaffold-constrained molecular decoration, and unconstrained property-guided optimization. While the first two are handled with no additional training, we propose a parameter-efficient fine-tuning method for the last task, which uses property-ordered molecular pairs as input. We call this new approach Pair-Tuning. Our results show GP-MoLFormer performs better or comparable with baselines across all three tasks, demonstrating its general utility for a variety of molecular generation tasks. We further report strong memorization of training data in GP-MoLFormer generations, which has so far remained mostly unexplored for chemical language models. Our analyses reveal that training data memorization and novelty in generations are impacted by the quality and scale of the training data; duplication bias in training data can enhance memorization at the cost of lowering novelty. We further establish a scaling law relating inference compute and novelty in generations.